ENGINEERING THERMODYNAMICS STUDY MATERIAL

Vishwatmak Om Gurudev College Of Engineering Thermodynamics the boiler. (a) Assuming the ideal processes, find per kg of steam the net work and cycle efficiency.(b) If the turbine and the pump have each 80% efficiency, find the percentage reduction in the net work and cycle efficiency. Sketch p-v and T-s diagrams. 10 MAY 2007 Q 5 (c) In a steam power plant the condition of steam at inlet to the steam generator is 20 bar and 300° C and the condenser pressure is 0.1 bar. Two feedwater heaters operate at optimum temperature. Determine (a).the quality of steam at exhaust, (b) network per kg of steam (c) cycle efficiency and (d) the steam rate. Neglect pump work 10 DEC 2007 Q 5 (c) In a steam power plant boiler, pressure is 60 bar and the condenser pressure is 0.07 bar. The steam temperature at boiler outlet is 550°C. Determine— (i) Turbine work per kg. (ii) Cycle’ efficiency (iii) Heat transfer in condenser per kg (iv) Mass flow rate of steam to produce 5 MW. 10 V O G C E MAY 2008 Q 4 (b) In a steam power plant boiler pressure is 60 bars and condenser pressure is 0.08 bars. The steam temperature at boiler outlet is 500°C. Determine:— (i) Turbine work per kg (ii) Heat transfer in condenser per kg (iii) Cycle efficiency (iv) Mass flow rate of steam to provide 5 MW. 12 DEC 2008(RC) Q 5 (a) In a reheat cycle steam at 500°C expands in H.P turbine till it is saturated vapour. It is reheated at constant pressure to 400°C and then expands in L.P. turbine to 40°C. If the maximum moisture content is limited to 15% at the turbine exhaust find —(i) reheat pressure (ii) the pressure of steam at inlet to H.P turbine (iii) net specific work output (iv) cycle efficiency (v) steam rate. Assume all ideal process and neglect feed pump work. 12 Prof.S Venkatesh Rao 151

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2009(RC) Q 6 (a) A steam Power station. uses the fallowing cycle. Steam at boiler outlet 150 bar and 550°C, reheat at 40 bar to 550°C, condenser at 0.1 bar. Find (i) Quality at turbine exhaust (ii) Cycle efficiency (iii) Steam rate. 12 DEC 2009(RC) Q6 (b) A steam turbine working on Rankine cycle is supplied with dry saturated steam at 25 bar and the exhaust takes place at 0.2 bar. For a steam flow rate of 10 kg/s, determine 1) quality steam at end of expansion, 2) turbine shaft work, 3) power required to drive the pump, 4) work ratio,5) Rankine efficiency. 10 MAY 2010(RC) Q3 (b) A Rankine cycle operates between the pressure 15 bar and 0.01 bar. The initial degree of superheat is 100 °C. Assuming isentropic efficiency of expansion 85%, calculate (i) Pump work (ii) Actual turbine work (iii) Thermal efficiency. 9 V O G C E DEC 2010(RC) Q6 (b) Steam is supplied to a turbine at a pressure of 32 bar and a temperature of 395 °C. It expands isentropically to a pressure of 0.08 bar. What is the dryness fraction at the end of expansion and the thermal efficiency? Calculate the modified condition and thermal efficiency if the steam is reheated at 5.5 bar to a temperature of 395 °C and then expanded isentropically to a pressure of 0.08 bar. MAY 2011(RC) Q 5 (b) A cyclic steam power plant is to be designed for steam temperature at inlet of 360° C and an exhaust pressure of 0.08 bar. After isentropic expansion of steam in the turbine, the moisture content at the turbine exhaust is not to exceed 15%.Determine the greatest allowable steam pressure at the turbine inlet and calculate the Rankine cycle efficiency for these steam conditions. Estimate also the mean temperature of heat addition. 10 Prof.S Venkatesh Rao 152

Vishwatmak Om Gurudev College Of Engineering Thermodynamics DEC 2011(RC) Q 5. (a) Steam at 20 bar, 350°C is expanded in a steam turbine to 0·1 bar. It then enters a condenser where it is condensed to saturated liquid water. The pump feeds back the water into the boiler. Determine Rankine efficiency and specific steam consumption of the power plant. Also find the Rankine efficiency when turbine and pump have efficiencies 0·8 and 0·75 respectively. 10 MAY 2012(RC) Q 5. (a) Steam turbine working on Rankine cycle is supplied with dry saturated steam at 25 bar and the exhaust takes place at 0·2 bar. For a steam flow rate of 1.0 kg/s. Determine : (i) quality steam at end of expansion (ii) turbine shaft work (iii) power required to drive the pump (iv) work.ratio (v) Rankine efficiency (vi) heat flow in the condenser. 12 V O G C E Prof.S Venkatesh Rao 153

Vishwatmak Om Gurudev College Of Engineering Thermodynamics CHAPTER 9 AIR STANDARD CYCLE 1. What are the assumptions made for Air standard Cycle? [MAY 2006, DEC 2010] 4 Marks Air standard cycles are based on the following assumptions. 1. The working fluid (air) behaves as a perfect gas and follows the gas laws. 2. All the processes that constitute the cycle are reversible. 3. The compression and expansion are strictly reversible adiabatic. 4. There is no heat losses from the system to the surroundings. 5. The specific heats Cp and Cv of air do not change with temperature. 6. There is no change in the mass of the working medium. 7. Heat is assumed to be supplied from a constant high temperature source and not from chemical reactions during the cycle. V O G C E 2. What is the compression ratio? [MAY 2008] 3 Marks It is the ratio of volumes of gas before and after isentropic compression in gas cycle and air standard efficiency of a cycle is directly proportional to this ratio. ������������������������������������������������������������������������������������������������������������������������������������ ������������������������������������������������������������, ������������ = ������������������������������������������������������������������������ ������������������������ ������������������������������������ ������������������������������������������������������������������������ ������������������������������������������������������������������������������������������������������������������������������������ = ������������1 ������������������������������������������������������������������������ ������������������������ ������������������������������������ ������������������������������������������������������������ ������������������������������������������������������������������������������������������������������������������������������������ ������������2 3. What is cut-off ratio? How does it affect the thermal efficiency of Diesel cycle? [MAY 2006, DEC 2006, MAY 2009, DEC 2009, MAY 2010, MAY 2011, MAY 2012], 4 Marks Prof.S Venkatesh Rao 154

Vishwatmak Om Gurudev College Of Engineering Thermodynamics The cutoff ratio rc, is defined as the ratio of the cylinder volumes after and before the combustion process in diesel cycle V ������������ = ������������3 O ������������2 G CAs efficiency of diesel cycle is given by E 1  ρ γ - 1    η = 1 - (r )γ −1  ρ - 1  Diesel γ So as the cutoff ratio decreases, the efficiency of the Diesel cycle increases as shown in fig Prof.S Venkatesh Rao 155

Vishwatmak Om Gurudev College Of Engineering Thermodynamics 4. Derive an expression of air standard efficiency for Otto cycle. [DEC 2009] 10 Marks • This cycle was introduced by German scientist Otto in 1876. The present day petrol (gasoline) engine operates on this cycle. • The Otto cycle on P-V and T-S diagram is shown in Figure. V O G C E • The point 1 represents that cylinder is full of air with pressure P1, volume V1 and absolute temperature T1. Process 1-2 • Represents adiabatic compression of air due to which P1, V1 and T1, change to P2, V2 and T2 respectively. Process 2-3 • Shows the supply of heat to the air at constant volume so that P2 and T2 change to P3 and T3. (V3 being the same as V2). Process 3-4 • Represents adiabatic expansion of the air. During expansion P3, V3 and T3 change to a final value of P4, V4 (=V1) and T4 respectively. Prof.S Venkatesh Rao 156

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Process 4-1 • Shows the rejection of heat by air at constant volume till the original state reaches. • Consider 1 kg of working substance (i.e. air). • Heat supplied at constant volume, Qs = Cv (T3 - T2 ) Heat rejected at constant volume, QR = CV (T4 - T1 ) Work done Now, Efficiency = Heat supplied =W Q -Q =s R V η otto Q Q O G ss C E ( )ηotto ( )∴ = Cv T3 - T2 - Cv (T4 - T1 ) Cv T3 - T2 ∴ ηotto = 1 - (T4 - T1 ) (T3 - T2 ) ..... (1) V Let, 1 = r = compression ratio V 2 V and 4 = Expansion ratio V 3 but V = V and V = V 14 23 VV ∴ 1 = 4 =r VV 23 For Process 1-2 T2 =  V1 γ −1 = (r )γ −1 T    V  1 2 ∴ T = T (r )γ −1 31 Substituting the value of T3 and T4 in equation (1) Prof.S Venkatesh Rao 157

Vishwatmak Om Gurudev College Of Engineering Thermodynamics ( )( )( )ηotto = 1- T4 - T1 r γ −1 T4 r γ −1 - T1 η otto = 1 - (T4 − T1 ) −1 (T4 - T1 ) (r )γ ∴ ∴η = 1 - (r 1 otto )γ −1 • This expression is known as air standard efficiency of the Otto cycle. • From above expression, it is clear that the thermal efficiency of the Otto cycle is a function of compression ratio ‘r’ and ratio of specific heats γ. • As ‘γ’ is constant for any working fluid, the efficiency is increased by increasing the compression ratio. Further, the efficiency is independent of heat supplied and pressure ratio. V O G C E 5. Show that the compression ratio for maximum work to be done per kg of air in an Otto cycle between upper and lower limits of absolute temperatures T3 and T1 is given by — [DEC 2007] 6 Marks OR Show that, for the maximum work to be done per kg of air in Otto cycle between given upper and lower limits of absolute temperature T3 and T1 respectively, the ratio of compression should have the value [DEC 2010, DEC 2011] 10 Marks The work done per kg of fluid in the cycle is given by Prof.S Venkatesh Rao 158

Vishwatmak Om Gurudev College Of Engineering Thermodynamics ……(1) This expression is a function of r when T3 and T1 are fixed. The value of W will be maximum when V O G C E Prof.S Venkatesh Rao 159

Vishwatmak Om Gurudev College Of Engineering Thermodynamics 6. Derive an expression of air standard efficiency for Diesel Cycle • This cycle was introduced by Dr. R Diesel in 1897. • It differs from Otto cycle, in that heat is supplied at constant pressure instead of constant volume. • The diesel cycle is also termed as constant pressure cycle. • The diesel cycle on P-V and T-S diagram is shown in Figure 2. • The cycle is described as follows V O G C E Process 1-2 • Represents adiabatic compression of air due to which P1, V1 and T1 change to P2, V2 and T2 respectively. Process 2-3 • During this process heat is supplied to the air at constant pressure so that V2 and T2 change to V3 and T3. (P2 being the same at P3). Process 3-4 • It represent adiabatic expansion of the air. • During expansion P3, V3 and T3 change to final value of P4, V4 (=V1) and T4 respectively. Prof.S Venkatesh Rao 160

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Process 4-1 • Shows the rejection of heat by air at constant volume till the original stage reaches.  Now, let us consider 1 kg of air.  Heat supplied at constant pressure, ( )Q = C T - T s p3 2  Heat rejected at constant volume, ( )Q = C T - T R V4 1 η = Work done ∴ Diesel Heat supplied η Diesel =W Q -Q =s R V Q Q ∴O ss ∴ G C ( ) ( )C T - T - C T - T E ( )η = P 3 2 v 4 1 Diesel C T -T P3 2 = 1- C  T -T   v 4 1  C  T -T  p 3 2 = 1 - 1  T -T  γ    4 1  ...... (i) T -T 3 2 • This gives the thermal efficiency in terms of temperatures. • Let ‘r’ be the compression ratio V r= 1 V2 and ‘ρ’ be the fuel cut off ratio. For adiabatic process 1-2 – T2  V1 γ −1 T1 V2 = = (r )γ −1 T = T (r )γ −1 21 …..(ii) Prof.S Venkatesh Rao 161

Vishwatmak Om Gurudev College Of Engineering Thermodynamics  For Constant pressure process 2-3 – V V =3 2 TT 23 VV 3 = 3 = ρ = fuel cut - off ratio TT ∴ 22 T = ρT ∴ 32 T = T (r )γ −1 but 2 1 T = T ρ (r )γ −1 ∴ 31 …..(iii) For adiabatic process 3-4 – V O T  V γ −1 G C 4 = 3 E T  V    3 4  V V γ −1  = 3 × 2   V V  2 4 =  V × V2  (V = V ) V  41 3  1  V  2 T =  ρ γ −1 V3 = V ρ and 1 = r 4 ∴ T r  V V  3 2 2 .  ρ γ −1  r  T = T ∴ 4 3 T = T .ρ (r )γ −1 . ρ γ −1 but 4 1 r ∴ T4 = T1 . ρ γ …..(iv) Now, substituting the values of T2, T3 and T4 from Equations (ii), (iii) and (iv) in Equation (i), we get, η = 1 - 1  T .ργ -T −1  γ   Diesel T1 . 11   ρ(r )γ −1 - T (r )γ 1 Prof.S Venkatesh Rao 162

Vishwatmak Om Gurudev College Of Engineering Thermodynamics η = 1- 1  ργ -1  γ   Diesel  ρ (r )γ −1 - (r )γ −1  ∴ 1  ρ γ - 1    η = 1- γ (r )γ −1  ρ - 1  Diesel ∴ 7. Derive the expression for cycle efficiency of Dual cycle. [DEC 2008] 8 Marks • In order to allow more time for the combustion of the fuel in a diesel engine without affecting the efficiency it is often arranged in engines of moderate power for injection of the fuel to commence before the end of the compression stroke, so that the combustion proceeds partly at constant volume and partly at constant pressure. Such a cycle is known as the ‘Dual combustion cycle’. • An engine working on this cycle is known as semi-diesel engine. • The P-V and T-S diagram for the dual combustion cycle is shown in the figure. V O G C E The dual combustion cycle has the following operations 1-2 : Reversible adiabatic compression 2-3 : Constant volume heat addition 3-4 : Constant pressure heat addition 4-5 : Reversible adiabatic expansion 5-1 : Constant volume heat rejection The air standard efficiency of this cycle can be calculated as usual Total heat added during the cycle. Prof.S Venkatesh Rao 163

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Qs = Heat added during process 2-3 + Heat added during process 3-4. ∴ Qs = Qs1 + Qs2 For unit mass of air, ( ) ( )Q = C T - T + C T - T s v32 p4 3 Heat rejected during process 5-1, ( )Q = C T - T R vS1 Now , Efficiency = Work done Heat supplied η Dual =W Q -Q Q =s R Q ∴ ss V O ( ) ( ) [ ]=C v  G T -T +C T -T  - C T -T C E 32 p4 3 v 5 1 ( ) ( )Cv  T -T +C T -T  32 p 4 3 ( )= 1 -  Cp  T5 - T1 γ =  ( ) ( )T -T 32 +γ   T -T C …..(i) 43 v = V1 V Let, Compression ratio, r 2 P =3 P Explosion ratio, α 2 Fuel cut off ratio, ρ V =4 V 3 For adiabatic process 1-2 – T  V γ −1 2 = 1 = (r )γ −1 T  V  …..(ii)   1 2 Prof.S Venkatesh Rao 164

Vishwatmak Om Gurudev College Of Engineering Thermodynamics For constant volume process 2-3 – P = P 2 3 TT 23 TP 3 = 3 =α T P ∴ 2 2 T T T= 3 or T = 3 ∴2 α 2 α …..(iii) Substituting the value of T2 from Equation (iii) in Equation (ii) T = (r )γ −1 T 3 3 or T = αr γ −1 αT1 1 ∴ …..(iv) V For constant pressure process 3-4 –O G C V V E =3 4 TT 43 TV 4 = 4 =ρ TV ∴3 3 T = ρT ∴ 4 3 …..(v) For adiabatic process 4-5 – T  V γ −1 4 = 5 T  V    5 4  V5 V3 γ −1 V4  =  V2 ×    V V γ −1  = 1 × 3   V V  2 4  r γ -1 ρ = …..(vi) V = V and V = V , Also V1 = r and V4 = ρ 23 51 V V Note - 23 Prof.S Venkatesh Rao 165

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Substituting the value of T4 from Equation (v) in Equation (vi) ρT =  r γ −1 ρ ∴ 3 T 5  ρ γ −1  r  T5 = ρ T3 ∴ …..(vii) Substituting the values of T1, T2, T4 and T5 in equation (i), we get, 1 - ρ T3 ρ r γ −1 - T3 α r γ −1 T3 - T3 α + γ ρ T3 E − T3 [ ] ( )( )ηDual= ( )= ρ ρ r γ -1 1 α r γ -1 1 - [1 − (1 α )]+ γ (ρ - 1) V  1  E  ρ γ − 1  O    α  G  (r )γ −1  C E = 1-  α− 1   α  + γ (ρ - 1) ( )= 1- 1 ×  α ρ γ -1   (r )γ −1  (α - 1) + α γ (ρ - 1) η = 1 - 1  α ρ γ - 1    Dual (r )γ −1  - 1)  (α - 1)+ α γ (ρ  8. Compare Otto, Diesel and Duel cycles for same compression ratio and for same heat supply with the help of P - V and T -S diagrams. [DEC 2005, DEC 2006] 6-8 Marks AND Compare Otto, Diesel and Dual cycles for constant maximum pressure and heat supplied. [DEC 2007] 3 Marks OR Compare the efficiency of the Otto, the Diesel and the Dual cycle under the condition of (i) equal compression ratio and heat input (ii) constant maximum pressure and heat input with neat sketch on T-s diagram. [DEC 2010] 6 Marks ALSO Prof.S Venkatesh Rao 166

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Compare the efficiency of the Otto, the Diesel and the Dual cycle under the condition of (i) equal compression ratio and heat rejection (ii) constant maximum pressure and heat rejection with neat sketch on T-s diagram. (a) If the Heat Supplied and the Compression Ratio is same: The three cycles on P-V and T-S diagrams are shown in Figure, if the compression ratio r and heat supplied is same for all the cycles. V O G C E Figure: Comparison of Otto, diesel and dual combustion cycles for same heat supplied and CR. 1-2-3-4 → Otto Cycle → Diesel Cycle → Dual cycle • Process (1-2) represents isentropic compression process. For the same heat supplied, if the compression ratio is same, the Otto cycle results in maximum pressure and temperature and for the diesel cycle these values are least while for the dual combustion cycle the values for pressure and temperature lies between the two. • Heat rejected is represented by the area under the curve on (T-S) diagram which equals to (a — 1 — 4 — b), (a — 1 — 4’’ — d) and Prof.S Venkatesh Rao 167

Vishwatmak Om Gurudev College Of Engineering Thermodynamics (a — 1 — 5’ — c) for Otto, Diesel and Dual cycles respectively while the heat supplied for each cycle remains the same. • It is evident that the heat rejected by Otto cycle is minimum and for the diesel cycle is maximum and for dual cycle the value lies between the two. • Since work done equals to difference of heat supplied and heat rejected and efficiency is ratio of work done to heat supplied, it follows that for the same compression ratio and heat supplied the Otto cycle has the maximum efficiency, the diesel cycle has the least efficiency and for dual cycle the value of efficiency lies between the values of Otto and Diesel efficiencies. η >η >η Otto Dual Diesel V O G C E (b) For Same Constant Maximum Pressure and Heat Supplied The following Fig. represents the (p-V) and (T-S) diagrams for Otto cycle and diesel cycle for of same constant maximum pressure and heat supplied. • For same maximum pressure (p3 = p3’) and for the same heat supplied, the area (a — 2’ —3’ — b) must be equal to area (a — 2 — 3 — c) as represented on (T-S) diagram. • The heat rejected by diesel cycle represented by area (b — 4’ — 1 — a) is less than the Otto cycle represented by area (c — 4 — I — a). Prof.S Venkatesh Rao 168

Vishwatmak Om Gurudev College Of Engineering Thermodynamics • Therefore it follows that the Diesel cycle efficiency is more than the Otto cycle efficiency for the case of same maximum pressure and heat supplied. • The dual cycle efficiency lies between the efficiency of diesel and Otto cycle. η >η >η Diesel Dual Otto (c) The Compression Ratio is same and the Heat Rejected The three cycles on P-V and T-S diagrams are shown in Figure V O G C E 1-2-3-4  Otto Cycle 1-2-7-4  Diesel Cycle 1-2-5-6-4  Dual Cycle • It is the fact that, for the same amount of heat rejection i.e. QR, the higher the amount of heat supplied Qs the higher will be the cycle efficiency. • In the T-S diagram, the area under 2-3 represents Qs for Otto cycles, the area under 2-7 represents Qs for the diesel cycles and the area under 2-5-6 represents Qs for the dual cycle. • Therefore, for the same compression ratio ‘r’, and heat rejection QR, the efficiency of Otto cycle is maximum and that of diesel cycle is the minimum. η >η >η Otto Dual Diesel Prof.S Venkatesh Rao 169

Vishwatmak Om Gurudev College Of Engineering Thermodynamics (d) For Same Constant Maximum Pressure and Heat Rejected Following figure shows the comparison of the three cycles for the same maximum pressure and temperature, the rejection is also kept as the same. V 1-5-3-4  Otto Cycle O 1-2-3-4  Diesel Cycle G 1-6-7-3-4  Dual Cycle C E In this case, the heat supplied Qs from the T-S plot will be Area under 5-3 for Otto cycles Area under 2-3 for diesel cycle Area under 6-7-3 for dual cycle Since heat rejected QR being the same, η >η >η Diesel Dual Otto 9. Write short notes on: Brayton cycle. [MAY 2010] 5 Marks OR In Brayton cycle, prove that Thermal Efficiency [MAY 2006] 4 Marks Prof.S Venkatesh Rao 170

Vishwatmak Om Gurudev College Of Engineering Thermodynamics The air standard Brayton cycle is the ideal closed system gas turbine cycle. The cycle consists of following four process – 1-2 Isentropic (reversible adiabatic) compression. 2-3 Constant pressure heat addition 3-4 Isentropic (reversible adiabatic) expansion 4-1 Constant pressure heat rejection. The Brayton cycle on P-V and T=S diagram is shown in the figure. V O G C E For unit mass of air, Heat supplied during process 2-3, ( )Qs = C p T3 - T2 Heat rejected during process 5-1, QR = Cp (T4 - T1 ) Thermal efficiency = Work done = W Heat supplied Q s Q -Q =s R Q s [ ]= C p (T3 - T2 ) + Cp (T4 - T1 ) Cp (T3 - T2 ) (T - T ) ( )η = 1 - 4 1 th T - T 32 Prof.S Venkatesh Rao 171

Vishwatmak Om Gurudev College Of Engineering Thermodynamics The above expression may be written as – T   4 -1 T1   T η = 1- 1 th T  T  3 -1 2  T2  T =  P  Now , 2 2 T  P  1   1 γ −1 T  P  γ Similarly, 3 = 3 T  P  4   4 but P = P and P = P 23 14 V O TT G 2= 3 C TT E ∴ 14 T = T 4 3 TT ∴ 12 TT 4= 3 TT Substituting 1 2 in the above equation for thermal efficiency and we get, T η = 1- 1 th T2  P γ -1 γ   = 1 - 1   P 2 P If 2 = Pressure ratio = r then PP 2 γ −1  1  γ  r  η = 1 - p th Prof.S Venkatesh Rao 172

Vishwatmak Om Gurudev College Of Engineering Thermodynamics 10. Derive an expression for optimum pressure ratio in a Brayton Cycle in terms of maximum and minimum cycle temperatures. V O G C E This is optimum pressure ratio in a Brayton Cycle in terms of maximum and minimum cycle temperatures. Prof.S Venkatesh Rao 173

Vishwatmak Om Gurudev College Of Engineering Thermodynamics FOR LAST MINUTE REVISION V O G C E Prof.S Venkatesh Rao 174

Vishwatmak Om Gurudev College Of Engineering Thermodynamics EXAMINATION QUESTIONS MAY 2005 Q 1 Fill in the blanks : For same compression ratio and same heat rejected write the thermal efficiencies in decreasing order for Diesel Otto and Dual cycles ______________ 1 Q 7 Write note on: (ii) For same maximum pressure and temperature compare Otto, Dual and Diesel cycles with P-V and T-S charts. 5 DEC 2005 Q 7 (b) Compare Otto, Diesel and Duel cycles for same compression ratio and for same heat supply with the help of P — V and T — S diagrams. 8 V O G C E MAY 2006 Q 1 (h) What is cut-off ratio? How does it affect the thermal efficiency of Diesel cycle? 3 Q 6 (a) In Brayton cycle, prove that Thermal Efficiency Where ,Rp, = pressure ratio 4 Q 6 (b) What are the assumptions made for Air standard Cycle? 4 DEC 2006 Q 6 (a) What is cut off ratio and explosion ratio? How does cut off ratio affect the thermal efficiency or Diesel cycle? 4 Q 6 (b) Compare Otto, Diesel and Duel cycles for same compression ratio and for same heat supply with the help of p-v and T-s diagrams. 6 MAY 2007 Q 6 (a) For same compression ratio and heat rejection, compare Otto, Diesel and Dual cycle with the help of p-v and T-s diagrams. 5 Prof.S Venkatesh Rao 175

Vishwatmak Om Gurudev College Of Engineering Thermodynamics DEC 2007 Q 1 (d) Compare Otto, Diesel and Dual cycles for constant maximum pressure and heat supplied. 3 Q 6 (a) Show that the compression ratio for maximum work to be done per kg of air in an Otto cycle between upper and lower limits of absolute temperatures T3 and T1 is given by — 6 MAY 2008 3 Q 1 (h) What is the compression ratio? V O G C E DEC 2008(RC) Q 5 (b) Derive the expression for cycle efficiency of Dual cycle. 8 MAY 2009(RC) 4 Q 1 (d) What is cut off ratio? How does it affect the thermal efficiency or Diesel cycle? DEC 2009(RC) Q1(e) What is cut-off ratio? How does it affect the air standard efficiency of a diesel cycle? 4 Q5 (b) Derive an expression of air standard efficiency for Otto cycle. 10 MAY 2010(RC) Q1 (e) What is Cut-off ratio ? How does it affect the thermal efficiency of Diesel cycle? 4 Q7. Write short notes on: (e) Brayton cycle. 5 DEC 2010(RC) Q1 (c) What are the assumptions for air standard cycle? 4 Q5(a) show that, for the maximum work to be done per kg of air in Otto cycle between given upper and lower limits of absolute temperature T3 and T1 respectively, the ratio of compression should have the value Prof.S Venkatesh Rao 10 176

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Q6 (c) Compare the efficiency of the Otto, the Diesel and the Dual cycle under the condition of (i) equal compression ratio and heat input (ii) constant maximum pressure and heat input with neat sketch on T-s diagram. 6 MAY 2011(RC) Q 1 (d) What is cut off ratio. Discuss its effect on the thermal efficiency of Diesel Engine. 5 Q 7 (c) Derive an expression for optimum pressure ratio in a Brayton Cycle in terms of maximum and minimum cycle temperatures. 4 DEC 2011(RC) Q 1. (a) Fill in the blanks :(iv) For same compression ratio and same heat rejection rate the thermal efficiency in decreasing order for Otto, diesel and dual cycles_______ 1 Q 6 (a) Show that the compression ratio for the maximum work to be done per kg 1 of air in an otto cycle between upper and lower limits of absolute temperatures T3 and T1 is given by V O G C E MAY 2012(RC) Q 1 (g) what is cut off ratio? How does it affect the· air standard efficiency of a diesel cycle? Q 6 (a) Prove the thermal efficiency of Otto cycle. 8 Prof.S Venkatesh Rao 177

Vishwatmak Om Gurudev College Of Engineering Thermodynamics GRADED PROBLEMS (A) OTTO CYCLE 1. An engine working on the Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. Heat supplied is 2100 kJ/kg. Calculate the maximum pressure and temperature of the cycle, the cycle efficiency and mean effective pressure. 8[DEC 2008(RC)] 2. A two cylinder, two stroke cycle engine working on the constant volume cycle has cylinder diameter of 35 cm and stroke 50 cm. The clearance volume ports are closed by the piston when it has travelled 8 cm from the dead centre on the compression stroke. The indicated mean effective pressure is 4.5 bar and the specific fuel consumption is 0.27 kg/kWh the calorific value of the fuel is 44000 kJ/kg. Calculate— (i) The indicated power at 180 rpm. (ii) The relative efficiency based on the effective compression ratio of the engine. 10[DEC 2004] V O G C E 3. An engine working on otto cycle has a volume of 0.45 m3, pressure 1 bar and temperature 300 C at the beginning of compression stroke. At the end of compression stroke, the pressure is 11 bar. 210 kJ of heat is added at constant volume. Determine (i) P,T and V at salient points in the cycle (ii) % clearance, (iii) Efficiency (iv) Net work per cycle (v) Power developed, if RPM = 210 10 [DEC 2003] 4. For the air standard Otto cycle with fixed intake and maximum temperature find the compression ratio that renders the work per cycle maximum. Find the expression foe maximum work and cycle efficiency at this compression ratio. Find these values if the intake and maximum temperatures are 27oC and 927oC respectively [DEC-94-8] . 5. An engine operates on the air standard Otto cycle. The conditions at the start of compression are 27oC and pressure 1 bar. The maximum temperature in the cycle is 3250 K. the compression Prof.S Venkatesh Rao 178

Vishwatmak Om Gurudev College Of Engineering Thermodynamics ratio is 8:1. Determine the pressure and temperature at salient points. Thermal efficiency and mean effective pressure. [DEC-95-8] (B) DIESEL CYCLE 6. In an air standard diesel cycle the stroke is 21 cm and diameter is 30 cms. Pressure and temperature at the start of the compression process is 100 KPa and 27°C. The cut-off takes place at 8% of the stroke and the compression ratio is 15. Find :— (i) Pressure and Temperature at all points. (ii) Heat added, Heat rejected and net work done. (iii) Air-standard efficiency. (iv) Mean effective pressure. 12 [MAY 2008] 7 A Diesel, engine has a compression ratio of 14 and cut-off takes place at 6% of the stroke. Find the air standard efficiency. 5 [MAY 2007] V O G C E 8. In an air standard Diesel cycle, the compression ratio is 15 and the fluid properties at the beginning of compression are 100 kPa and 300K. For a peak temperature of 1600K, calculate a) the percentage of stroke at which cut off occurs, b) the cycle efficiency and, c) the work out per kg of air. 10 [DEC 2009] (C) DUAL CYCLE 9. The swept volume of an engine working on Dual cycle 0.0053 m3 and clearance volume is 0.00035 m3. The maximum pressure is 65 bar. Heat addition ends at 5% of the stroke. The temperature and pressure at the beginning of compression are 80°C and 0.9 bar respectively. Determine the air standard efficiency of the cycle. 8 [MAY 2009(OC), DEC 2005] 10. An air standard dual cycle has a compression ratio of 15 and compression begins at 1 bar, 40° C. The maximum pressure is 65 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Estimate (a) the pressure and temperatures at the cardinal points of the cycle (b) the cycle efficiency and (c) the m.e.p.of the cycle, Cv =0.718 kJ/kg K, CP=1.005 kJ/kg K 10[DEC 2006, DEC 2005, MAY 2005, MAY 2009(RC), DEC 2008(OC)], MAY 2007] Prof.S Venkatesh Rao 179

Vishwatmak Om Gurudev College Of Engineering Thermodynamics 11. An engine working on Dual cycle has compression ratio 12, pressure and temperature at the beginning of compression are 1 bar and 320 K, percentage volume increase during constant pressure heating is 38. If it is assumed that Cp = 1 (kJ / kg – K) and C v = 0.714 (kJ/ kg K).Find the temperature at the end of expansion and m.e.p. [MAY-94-8] 12. An air standard dual cycle has a compression ratio of 6 and pressure and temperature at the beginning of compression are 1 bar and 27oC. After constant volume heat addition the temperature becomes 1177oC and constant pressure heat addition raises the temperature to 1627oC. Determine i. cut-off ratio ii. constant volume pressure ratio iii. expansion ratio iv. heat added and rejected v. thermal efficiency. [DEC-97-7] V O G C E 13. In air standard dual cycle, the air is at a pressure of 100 kPa and a temperature of 27oC before the isentropic compression begins. In this process, the volume of air is reduced from 0.07 m3 to 0.004 m3. During the process of heat addition at constant pressure, the temperature of the air is increased from 1160 to 1600oC. Determine i. Compression ratio ii. Cut – off ratio iii. Thermal efficiency iv. Mean effective pressure. [DEC-98-8]: (D) BRAYTON CYCLE 14. Obtain an expression for the specific work output of a gas turbine unit in terms of pressure ratio, isentropic efficiencies of the compressor and turbine, and the maximum and minimum temperature. T3 and T1. Hence show that the pressure ratio rp for maximum power is given by Prof.S Venkatesh Rao 180

Vishwatmak Om Gurudev College Of Engineering Thermodynamics If T3 = 1073 K, T1 = 300 K, ηC = 0.8, ηT =0.8 and γ= 1.4. Compute the optimum value of pressure ratio, the maximum net work output per kg of air, and corresponding cycle efficiency. 10 [DEC 2004] 15. In a gas turbine plant working on the Brayton cycle the air at the inlet is at 27°C, 0.1 MPa. The pressure ratio is 6.25 and the maximum temp. is 800°C. The turbine and compressor efficiency are each80%. Find — i) the compressor work per kg of air. (ii) the turbine work per kg of air. (iii) the heat supplied per kg of air. (iv) the cycle efficiency. 8 [MAY 2003] V O G C E Prof.S Venkatesh Rao 181

Vishwatmak Om Gurudev College Of Engineering Thermodynamics EXAMINATION PROBLEMS (SOLVE AS HOME WORK) MAY 2005 Q 4 (c) An air standard dual cycle has a compression ratio of 16, and compression begins at 1 bar, 50°C. The maximum pressure is 70 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Find— (i) Pressures and temperatures at the cardinal points of the cycle (ii) Cycle efficiency (iii) The mep of the cycle. 10 V O G C E DEC 2005 Q 5 (b) The swept volume of an engine working on Duel cycle is 0.0053 m3 and clearance volume 0.00035 m3. The maximum pressure is 65 bar. Heat addition ends at 5% of the stroke. The temperature and pressure at the beginning of compression are 80°C and 0.9 bar respectively. Determine the air standard efficiency of the cycle 8 MAY 2006 Q 6 (c) In an air standard diesel cycle the stroke is 30 cm and diameter is. 25 cm. Pressure and temperature at the start of the compression process is 100 KPa and 27°C. The cut-off takes place at 8°/o of the stroke and the compression ratio is 16. Find (i) Pressure and Temperature at all points (ii) Heat added, Heat rejected and network done (iii) Air standard efficiency. (iv). Mean effective pressure 12 DEC 2006 Q 6 (c) An air standard dual cycle has a compression ratio of 15 and compression begins at 1 bar, 40° C. The maximum pressure is 65 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Estimate (a) the pressure and temperatures at the cardinal points of the cycle (b) the cycle efficiency and (c) the m.e.p. of the cycle, Cv =0.718 kJ/kg K, CP=1 .005 kJ/kg K 10 Prof.S Venkatesh Rao 182

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2007 Q 6 (b) A Diesel, engine has a compression ratio of 14 and cut-off takes place at 6% of the stroke. Find the air standard efficiency. 5 Q 6 (c) An air standard dual cycle has a compression ratio of 16 and compression begins at 1 bar 50° C. The maximum pressure is 70 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Estimate. (i) The pressure and temperatures at he cardinal points of the cycle . (ii) The cycle efficiency and (iii) The m.e.p. of the cycle. 10 DEC 2007 V O G C E Q 6 (c) An engine with 300 mm stroke and 250 mm cylinder diameter works on theoretical Diesel cycle. Pressure and temperature at the, start of the compression process is 100 kPa and 30° C. The cut-off takes place at 8% of the stroke, the compression ratio is 16.Find (I) Pressure, and temperature at all points (ii) Heat added, Heat rejected and network done (iii) Theoretical air standard efficiency. 8 MAY 2008 Q 5 (b) In an air standard diesel cycle the stroke is 21 cm and diameter is 30 cms. Pressure and temperature at the start of the compression process is 100 KPa and 27°C. The cut-off takes place at 8% of the stroke and the compression ratio is 15. Find :— (i) Pressure and Temperature at all points. (ii) Heat added, Heat rejected and net work done. (iii) Air-standard efficiency. (iv) Mean effective pressure. 12 DEC 2008(RC) Q 5 (b) An engine working on the Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. Heat supplied is 2100 kJ/kg. Calculate the maximum pressure and temperature of the cycle, the cycle efficiency and mean effective pressure. 8 Prof.S Venkatesh Rao 183

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2009(RC) Q 5 (a) An air standard Dual cycle has a compression ratio of 16 and compression begins at 1 bar and 50°C. The maximum pressure is 70 bar. The heat transferred to air at constant pressure is equal to that a constant volume. Estimate (i) Cycle efficiency (ii) mean effective pressure of cycle. 12 DEC 2009(RC) Q6 (a) In an air standard Diesel cycle, the compression ratio is 15 and the fluid properties at the beginning of compression are 100 kPa and 300K. For a peak temperature of 1600K, calculate a) the percentage of stroke at which cut off occurs, b) the cycle efficiency and, c) the work out per kg of air. 10 V O G C E MAY 2010(RC) Q6. (a) In an engine working on Dual cycle, the temperature and pressure at the beginning of the cycle are 90 °C and 1 bar respectively. The compression ratio is 9. The maximum pressure is limited to 68 bars and total heat supplied per kg of air is 1750 KJ. Determine (i) Pressure and temperature at all salient points. (ii) Air standard efficiency (iii) Work done per cycle. 10 DEC 2010(RC) Q5(b) A diesel engine has 20 cm bore and 30 cm stroke. The clearance volume is 420 cm3. The fuel is injected at constant pressure for 5% of the stroke. Calculate the air standard efficiency. If the cut-off is delayed from 5% to 8% what will be the percentage loss in efficiency. In both cases, the compression ratio is the same. 10 MAY 2011(RC) NIL DEC 2011RC) Q 6 (b) The peak pressure in an otto cycle is 21 bar and the minimum pressure is 1 bar with thermal efficiency of 47·5% find- (i) Compression ratio (ii) Mean effective pressure. 10 Prof.S Venkatesh Rao 184

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2012(RC) Q 6 (b) In an air standard diesel cycle the stroke is 30 em and dia. is 25 ems. Pressure and temperature at the start of compression is 100 kPa and 270 C. The cut off takes place at 8% of the stroke and the compression ratio is 16. Find (i) Pressure ·and. temperature at all points. (ii) Heat added, heat rejected and net work done. (iii) Mean· effective pressure. 12 V O G C E Prof.S Venkatesh Rao 185

Vishwatmak Om Gurudev College Of Engineering Thermodynamics CHAPTER 10 REACTIVE SYSTEMS 1. Define clearly: 1. Lower Calorific Value. [DEC 2003, DEC 2008] 2. Higher Calorific Value. [DEC 2003, MAY 2006, MAY 2007, DEC 2008, MAY 2009] 3. Enthalpy (or Heat) of reaction (or Combustion) [DEC 2003, MAY 2004, DEC 2004, DEC 2005, MAY 2006, MAY 2007, DEC 2007, MAY 2008, MAY 2009] 4. Enthalpy (or Heat) of formation. [DEC 2003, MAY 2004, DEC 2004, DEC 2005, MAY 2008, MAY 2009] 5. Reactive and non-reactive system [DEC 2004, DEC 2005, MAY 2006] 6. Internal energy of reaction [DEC 2004, DEC 2005] 7. Adiabatic flame temperature [MAY 2004, MAY 2006, MAY 2007, DEC 2007, MAY 2008, DEC 2009] 8. Excess air [MAY 2004, DEC 2007, MAY 2008] 9. Stoichiometric air or theoretical air [MAY 2007, DEC 2007, DEC 2008, MAY 2009] 10. Calorific value at constant pressure &at constant volume [MAY 2004, MAY 2008] V O G C E I) LOWER CALORIFIC VALUE: Lower calorific value of a fuel is defined as a fictitious quantity of heat that would be obtained due to combustion of unit quantity of fuel if the water vapour formed in the products of combustion is cooled back to S.T.P. conditions and still remains in gaseous state. (II) HIGHER CALORIFIC VALUE: Higher calorific value of fuel is defined as the amount of heat released due to combustion of unit quantity of fuel when the products of combustion are cooled back Prof.S Venkatesh Rao 186

Vishwatmak Om Gurudev College Of Engineering Thermodynamics to standard temperature (25° C) and standard pressure (1 atm) called S.T.P. conditions. Water vapour formed will be in liquid state. III) ENTHALPY OF REACTION: The heat energy released due to complete combustion of unit quantity of fuel in a constant pressure process when products of combustion are cooled up to S.T.P. is called the enthalpy(or heat) of reaction(or combustion). (IV) ENTHALPY OF FORMATION: Enthalpy of formation of a chemical compound is defined as the increase in enthalpy when a compound is formed from its constituent elements in natural form and in standard state. (T0 = 25° C, p0 = 1 atm.) V O G C E (V) REACTIVE AND NON-REACTIVE SYSTEM  If there are no chemical reactions between the constituents of system, such a system is called non-reactive system.  However, if the constituents react and form new compounds, the system is called a reactive system. e.g. If C and 02 are supplied to a system, they form CO with release of chemical energy. (VI) INTERNAL ENERGY OF REACTION The heat energy released due to complete combustion of unit quantity of fuel in a constant volume process when the products of combustion are cooled back to S.T.P. is called the internal energy of reaction. (VII) ADIABATIC FLAME TEMPERATURE The temperature attained by the products of combustion in an adiabatic process due to complete combustion of fuel in the absence of work transfer or changes in K.E. and P.E. is called adiabatic flame temperature Prof.S Venkatesh Rao 187

Vishwatmak Om Gurudev College Of Engineering Thermodynamics (VIII) EXCESS AIR In order to achieve complete combustion of fuel as for as possible, more air than theoretical amount is required to be supplied and it is called excess air 2. Why excess air is always required to be supplied for combustion? State the factors on which the magnitude of excess air depends. [MAY 2003] 3 Marks • In practice, the combustion of fuel is never complete in case only the theoretical air is supplied due to imperfect mixing of fuel with air. • In view of this, in order to achieve complete combustion of fuel as for as possible, excess air is always supplied for combustion. • The magnitude of excess air supplied depends on o the density of mixture, o method of mixing and o turbulence present during the combustion. V O G C E 3. What do you understand by adiabatic flame temperature? What is its importance in the design of a combustor? How is it controlled? Explain the factors which affect it. [MAY 2003, DEC 2004] 5 Marks • Definition: The temperature attained by the products of combustion in an adiabatic process due to complete combustion of fuel in the absence of work transfer or changes in K.E. and P.E. is called adiabatic flame temperature. • This temperature is helpful in designing the combustion chambers from metallurgical considerations. • Adiabatic flame temperature can be controlled by the amount of excess air supplied. • Factors affecting the adiabatic flame temperature are o the type of fuel the work transfer, o kinetic and potential energy of the mixture entering into the system and the gases leaving the system, heat losses and o temperature of air and gases at entry and exit respectively. Prof.S Venkatesh Rao 188

Vishwatmak Om Gurudev College Of Engineering Thermodynamics 4. Write short note on: Heat of combustion in closed system. [MAY 2003] 6 Marks • In a combustion process, the reactants i.e. the mixture of fuel and air react on their combustion and the chemical energy is released with formation of products of combustion. • The total energy released on combustion in a closed system per kg of fuel depends the temperature at which the combustion process is carried out and the temperature of products of combustion. • The heat energy released by the fuel due to combustion in a closed system is called the heat of combustion. V O G C E 5. `Write short note on: Calorific value at constant pressure and constant volume. [MAY 03, MAY 04] 6 Marks Calorific value at constant pressure and at constant volume: • The heat energy released in constant pressure combustion when the products are cooled back up to S.T.P. is called calorific value of fuel at constant pressure, Qp. • In case the combustion is carried out at constant volume, the heat energy released is called the calorific value of fuel at constant volume, Qv • Qp andQv are related by the following equation, Where np= Number of moles of products of combustion nR= Number of moles of reactants Ro= universal gas constant = 8.3 143 kJ/mole K T= absolute temperature, Kelvin 6. What do you understand by adiabatic flame temperature? What is its importance in the design of a combustor? How is it controlled? Explain the factors which affect it. [MAY 2003] 5 Marks Prof.S Venkatesh Rao 189

Vishwatmak Om Gurudev College Of Engineering Thermodynamics OR Define adiabatic flame temperature. A fuel is burnt with (i) Theoretical air (ii) Excess air (iii) Deficiency of air. In which of the above three cases the adiabatic flame temperature will be the highest and why? Justify your answer. [MAY 2005] 8 Marks OR Write short notes on: Adiabatic combustion temperature. [DEC 2003] OR Discuss and explain the following: (a) Importance of adiabatic flame temperature in the design of combustion chamber [MAY 2009] 5 Marks • Adiabatic flame temperature is defined as the temperature of products in aV combustion process which takes place adiabatically without any work interactionO or changes in kinetic or potential energy.G C • Thus adiabatic flame temperature is the maximum possible temperature that can beE achieved for any combustion process. • Any heat transfer from the reacting substance or incomplete combustion would tend to lower the temperature of products. • Thus for any given fuel at given pressure and temperature of the reactants, the maximum adiabatic temperature that can be achieved is with a stoichiometric mixture. • The adiabatic flame temperature can be controlled by amount of excess air. • Control of adiabatic flame temperature is important in case of thermal equipment such as turbines where maximum temperature is determined by metallurgical considerations. • The adiabatic flame temperature curve is as shown in the figure. • It is a characteristic bell shaped curve with the maxima being the stoichiometric point. At this point the adiabatic flame temperature is achieved for a stoichiometric A/F ratio. Prof.S Venkatesh Rao 190

Vishwatmak Om Gurudev College Of Engineering Thermodynamics • If excess air is added to the stoichiometric A/F ratio, the A/F increases at the costV of temperature.O G • Still some excess air is used as it reduces the temperature and ensures completeC combustion without any unburned fuel trace in the flue gas. The region of excessE air is called “fuel lean” region. • If air supplied is less than stoichiometric then incomplete combustion takes place. • There is unburned fuel in the flue gas which is not desirable. • This region of deficient air is called “fuel rich” region. Most combustion equipment is operated in the fuel — lean region. 7. Discuss and explain the following: Heating Values of Fuels [ DEC 2007. MAY 2007, DEC 2007, DEC 2008] 5 Marks Definition of calorific value of fuel ( or Heating Value) The calorific value of a fuel can be defined as the heat energy released during complete combustion of unit quantity of fuel when the products of combustion are cooled back at S.T.P. Its unit are kJ/kg or kJ / kg mole (for solid and liquid fuels) or kJ/m3 (for gaseous fuels). The fuels containing hydrogen as one of the constituent will produce water vapour during combustion process. During the calorimetric measurements when the products of combustion are cooled back to their standard temperature, the enthalpy of vaporisation of steam would be given off to the water jacket of the calorimeter. The Prof.S Venkatesh Rao 191

Vishwatmak Om Gurudev College Of Engineering Thermodynamics calorific value so obtained is called higher or gross calorific value (H.C.V.) of fuels or higher heat of reaction. Whereas, the lower calorific value (L.C.V.) of the fuels is a fictitious quantity that would be obtained due to combustion of unit quantity of fuel if the water vapour formed in the products of combustion are cooled back to 25°C at atmospheric pressure and still remains in gaseous state. The relation between higher and lower calorific value of fuels is as follows: -Lower calorific value (LC.V.) = - Higher calorific value (H.C.V.) -mw x L where, mw = Mass of water vapour formed per kg of fuel L = Latent heat of vaporisation and part of sensible heat L = 2445 kJ/kg of water vapour at constant pressure L = 2308 kJ/kg of water vapour at constant volume V O G C E Prof.S Venkatesh Rao 192

Vishwatmak Om Gurudev College Of Engineering Thermodynamics EXAMINATION QUESTIONS MAY 2003 Q 1(a) Why excess air is always required to be supplied for combustion? State the factors on which the magnitude of excess air depends. (3M) (b) What do you understand by adiabatic flame temperature? What is its importance in the design of a combustor? How is it controlled? Explain the factors which effects it. (5 M) DEC 2003 Q 1(a) Define clearly. (i) Lower Calorific Value. (ii) Higher Calorific Value. (iii) Enthalpy of reaction. (iv) Enthalpy of formation. (8 M) Q 5 Write short notes on: (a) Adiabatic combustion temperature. (d) Entropy changes for a reactive mixture. (10 M) V O G C E MAY 2004 Q 4(a) Define following terms (i) Heat of reaction (ii) Heat of formation (iii) Calorific value at constant pressure and constant volume (iv) Excess air (v) Adiabatic flame temperature. (10 M) DEC 2004 Q 1(a) Discuss and explain the following: (i) Entropy change for reactive mixtures. (5 M) Q 2(a) Define the following: (10 M) (i) Reactive and non-reactive systems. (ii) Enthalpy and internal energy of reaction. (iii) Heat of combustion. (iv) Enthalpy of formation. MAY 2005 Q 2(a) Define Adiabatic flame temperature. A fuel is burnt with (i) Theoretical air (ii) Excess air (iii) Deficiency of air. In which of the above three cases the adiabatic flame temperature will be the highest and why? Justify your answer. (8 M) Prof.S Venkatesh Rao 193

Vishwatmak Om Gurudev College Of Engineering Thermodynamics DEC 2005 Q 1 Fill up the blanks: (a) During combustion of fuel, dilution of co-efficient is ratio of___________________ (b) Percentage of excess air is the ratio of _________________(4 M) Q 2(a) Define the following: (i) Reactive and Non-reactive Systems. (ii) Heat of Combustion. (iii) Enthalpy and Internal Enery of Reaction. (iv) Enthalpy of Formation. (8M) MAY 2006 Q 1(a) Discuss and explain the following: (i) Application of first law to reactive systems. Q 2(a) Define the following: (i) Higher calorific value (ii) Adiabatic flame temperature. (iii) Enthalpy of reaction (iv) Reactive and non-reactive systems. (8M) V O G C E DEC 2006 Q 1 Discuss and explain the following: (d) Heating values of fuels (5 M) Q 7(a) Explain in brief (i) Stiochiometric Air MAY 2007 Q 1 Discuss and explain the following : (c) Heating values of fuels(5 M) Q 5(a) Define the following (i) Enthalpy of reaction (iii) Higher calorific value (ii) Adiabatic flame temperature (iv) Theoretical air (8M) DEC 2007 Q 1 Discuss and explain the following : (d) Heating values of fuels (5 M) Q 7(a) Explain the following : (i) Stoichiometric air (ii) Access air (iii) Adiabatic flame temperature (iv) Enthalpy of reaction. (8M) Prof.S Venkatesh Rao 194

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2008 Q 1(a) Explain and discuss the following: (iv) Application of first law to reactive system (5 M) Q 4(a) Define the following terms: (i) Heat of reaction ii) Heat of formation iii) Calorific value at const. pressure & const. Volume iv) Excess air v) Adiabatic flame temperature (10M) DEC 2008 Q 1 Discuss and explain the following: (b) Heating Values of Fuels (5 M) Q 7(a) Define clearly — (i) Lower calorific value (ii) Higher calorific value (iii) Adiabatic Flame temperature. and (iv) Stoichiometric Air. (8M) V O G C E MAY 2009 Q 1. Discuss and explain the following: (a) Importance of adiabatic flame temperature in the design of combustion chamber (5 M) Q 2(a) Define :— (i) Enthalpy of reaction (ii) Enthalpy of formation (Hi) Higher heating value of fuel (iv) Stoichiometric air (4M) DEC 2009 Q 1 (a) Discuss and explain the following: Heating values of fuel. (5M) Q 2(a) Define :— (i) Enthalpy of combustion. (ii) Calorific value at constant pressure and constant volumes. (iii) Adiabatic combustion temperature. (iv) Actual air fuel ratio. Q 7 Write notes on: (c) Entropy changes for reacting mixtures. (5M) Prof.S Venkatesh Rao 195

Vishwatmak Om Gurudev College Of Engineering Thermodynamics MAY 2010 Q1: Discuss and explain: (a) Higher and lower heating value of fuel. (5M) Q 2. (a) Define :— (i) Enthalpy of combustion (ii) Enthalpy of formation (iii) Stoichiometric air fuel ratio (iv) Importance of adiabatic flame temperature. DEC 2010 Q1: Discuss & explain: A) Entropy change of reacting mixtures. (5M) Q2) A) Short note on:- I. Adiabatic flame temperature. II. Theoretical and actual combustion process. (4M) V O G C E Prof.S Venkatesh Rao 196

Vishwatmak Om Gurudev College Of Engineering Thermodynamics GRADED PROBLEMS WITHOUT WORK OUTPUT 1. Liquid octane C8 H18 at 25°C is used as fuel in a gas turbine plant. Air used is 180 percent of the theoretical and is supplied at 250C. Assuming complete combustion and the products leave the combustion chamber at 1600 K, calculate- 1. A : F ratio 2. Heat transfer per kg mol of fuel used. Use the following table. Temperature are in Kelvin. V O G C E WITH WORK OUTPUT 2. A gasoline engine delivers 150 kW. The fuel used is C8 H18 (L) and if enters the engine at 25°C. 150% theoretical air is used and it enters at 45°C. The products of combustion leave the engine at 1000K, and the heat transfer from the engine is 205 kW. Determine 1. the fuel consumption per hour, 2. A : F ratio If completes combustion is achieved. WITH WORK OUTPUT & K.E. CHANGE 3. A small gas turbine uses C8H18(l) for fuel. It delivers 2 MW power. The air and fuel enters at 25°C and the product of combustion leaves at 1000 K. Following observation was made during a test— Prof.S Venkatesh Rao 197

Vishwatmak Om Gurudev College Of Engineering Thermodynamics Air = 300% of theoretical at 25°C Velocity of air at inlet = 70 m/s Velocity of product at exit = 700 m/s Heat transfer from the system = 150 kW. Determine the fuel consumption per hour, if the complete combustion is achieved. Given data:— V O G C E INCOMPLETE COMBUSTION 4. Ethane (C2H6) at 25°C is burned in a steady flow combustion chamber with 20% excess air at 127°C, but only 95% of the carbon is converted to CO2. If the products leave at 1200°K, calculate the heat transfer. The pressure remains constant at later. Use the following data: (i) Enthalpy of formation (h0f) in kJ/k mol Ethane (g) = (— 84680) Carbon dioxide (g) = (— 393520) Carbon monoxide (g) = (— 110530) Water (g) = (— 241820) Water (L) = (— 285830) (ii) Enthalpy (h) in kJ/k mol at various temperatures Prof.S Venkatesh Rao (12 M) 198

Vishwatmak Om Gurudev College Of Engineering Thermodynamics ADIABATIC FLAME TEMPERATURE 5. Liquid Octane at 30°C is burned with 400% theoretical air at 30°C in a steady flow process. Determine the adiabatic flame temperature. CHEMISTRY OF COMBUSTION 6. The products of combustion of an unknown hydrocarbon CxHy a have the following composition as measured by orsat apparatus CO2 = 8%, CO = 0.9%.,O2 = 8.8% and N2 = 82,3% Determine: (a) Composition of the Fuel (b) Air Fuel Ratio (c) Percentage excess air used V O G C E 7. Fuel oil has following analysis by mass C — 85%, H2 — 12.5%, O2—2% and residue — 0.5%. The dry flue gas has following composition by volume — CO2—9%, CO — 01% O2 - 7.77%, N2 — 82.25%. Determine air fuel ratio.(12 M) 8. The percentage analysis of gaseous fuel by volume is given as follows; C02=8%, CO=22%, O2=4% & N2=36% Determine the minimum volume of air required for complete combustion of 1m3 of gas and calculate the percentage combustion by volume of the dry products of combustion. If 1.4m3 of air is supplied per m3 of gas, what will be the percentage by volume of CO2 in the dry products of combustion? (10 M) Prof.S Venkatesh Rao 199

Vishwatmak Om Gurudev College Of Engineering Thermodynamics EXAMINATION PROBLEMS (HOME WORK) MAY 2003 1. A small gas turbine uses C8 H18 (l) for fuel. It delivers 2 MW power. The air and fuel enters at 25°C and the products of combustion leave at 1000 K. Following observation were made during a test — Air = 300% of theoretical at 25°C Velocity of air at inlet = 70 m/s Velocity of product at exit = 700 m/s Heat transfer from the system = 150 kW. Determine the fuel consumption per hour, if the complete combustion is achieved. Give data: V O G C E DEC 2003 2. A gasoline engine delivers 150 kW. The fuel used is C8 H18 (L) and it enters the engine at 25°C. 150% theoretical air is used and it enters at 45°C. The products of combustion leave the engine at 750 K, and the heat transfer from the engine is 205 kW. Determine the fuel consumption per hour, if complete combustion is achieved. Enthalpy of formation, Gibbs function of formation at 25°C and 1 atm press: (8 M) MAY 2004 3. One K mole of methane gas (CH4) is burnt completely with 10% excess air in a constant volume container. Before combustion, both methane and air are at 25°C at 1 atm. The combustion products are at 150°C at end of combustion. Determine the heat transfer during the process. Given: Prof.S Venkatesh Rao 200