Thermo

Question 1

Self ignition would occur in the engine using certain brand of petrol if the temperature due to compression reached 350°C.

Calculate the highest ratio of compression that may be used to avoid pre-ignition if the law of compression is

PV 1 . 3 = c

PV 1 . 4 = c

Calculate the final pressure in each case. Assume inlet condition of 27°C and 1 bar.

Answer 1

a 23.5 bar
b 12.8 bar

Question 2

Self-ignition would occur in an engine using certain brand of petrol if the temperature due to compression reaches 350o C; when the inlet condition is 1 bar, 27o C.

Calculate the highest compression ratio possible in order to avoif self-ignition, if the compression is according to

a) adiabatic, with index of 1.4; and

b) polytropic, with index of 1.3

Answer 2

a 6.2
b 11.4

Question 3

The model ‘6SE-TCA3 Perkins’ diesel engine have a stroke of 190 mm and a bore of 160 mm. If its clearance volume is 5% of the swept volume, determine the pressure and temperature at the end of compression when the inlet condition is 1 bar, 27o C.

Answer 3

P 67.2 bar
T 956 K

Question 4

The model ‘6SE-TCA3 Perkins’ diesel engine have a stroke of 190 mm and a bore of 160 mm. If its clearance volume is 5% of the swept volume, determine the pressure and temperature at the end of compression when the inlet condition is 1 bar, 27o C.

Answer 4

P 67.2 bar
T 956 K

Question 5

A closed rigid container has a volume of 1 m 3 and holds air at 345 kPa and 20°C. Heat is added until the temperature is 327°C. Determine the change in Internal Energy:-

a) Using an average value of the specific heat.

b) Taking into account the variation of specific heat with temperature.

Answer 5

a 932 kJ
b 1018.7 kJ

Question 6

An adiabatic steam turbine expands steam from a pressure of 6 MPa and a temperature of 500°C to a pressure of 10 KPa The isentropic efficiency of the turbine is 0.82 and changes in kinetic and potential energy may be neglected. Determine the state of the steam at exit from the turbine and the specific work transfer.

Answer 6

849 kJ/kg

Question 7

A steam turbine receives steam at 2 MPa and 250o C, and exhausts at 0.1 MPa, 0.85 dry.

a) Neglecting heat losses and changes in ke and Pe, estimate the work output per kg steam.

b) If, when allowance is made for friction, radiation, and leakage losses, the actual work obtained is 80% of that estimated in (a), calculate the power output of the turbine when consuming 600 kg of steam per minute.

Answer 7

a 539 kJ/kg
b 4.31 MW

Question 8

A boiler receives feed water at 40o C and delivers steam at 2 MPa and 500o C. If the furnace is oil fired, the calorific value of oil being 42000 kJ/kg and 4000 kg oil are burned while 45000 kg of steam are produced, determine :

a) the heat supplied in the boiler.

b) the efficiency of the boiler.

Answer 8

a 1.484 x 10^8 kJ
b 88%

Question 9

An air compressor receives air at 27o C and delivers it to a receiver at the rate of 0.5 kg/s. It is driven by an electric motor which absorbs 10 kW and the efficiency of the drive is 80%.

Water jacket cooling is used at the rate of 6 kg/min while its temperature rises from 10o C to 20o C. Estimate the temperature of the air delivered.

Data : Cp w = 4.186, and Cp a = 1.005 kJ/kgK

Answer 9

43.5 C

Question 10

An air compressor receives air at 27o C and delivers it to a receiver at the rate of 0.5 kg/s. It is driven by an electric motor which absorbs 10 kW and the efficiency of the drive is 80%.

Water jacket cooling is used at the rate of 6 kg/min while its temperature rises from 10o C to 20o C. Estimate the temperature of the air delivered.

Data : Cp w = 4.186, and Cp a = 1.005 kJ/kgK

Answer 10

43.5 C

Question 11

Air at 27o C receives heat at constant volume until its temperature reaches 927o C. Determine the heat added per kilogram? Assume for air C V = 0.718 kJ/kgK.

Answer 11

646.2 kJ/kg

Question 12

An insulated, constant-volume system containing 1.36 kg of air receives 53 kJ of paddle work. The initial temperature is 27o C. Determine

Q = 0 ( insulated system ) W = -53 kJ ( externally inputted work ) The change in internal energy ∆U is

a) the change of internal energy.

b) the final temperature.

Assume a mean value C v = 0.718 kJ/kgK.

Answer 12

a 53
B 81.3

Question 13

An ideal gas occupies a volume of 0.5 m 3 at a temperature of 340 K and a given pressure. The gas undergoes a constant pressure process until the temperature decreases to 290 K. Determine

a) the final volume,

b) the work if the pressure is 120 kPa An ideal gas occupies a volume of 0.5 m 3 at a temperature of 340 K and a given pressure. The gas undergoes a constant pressure process until the temperature decreases to 290 K. Determine

a) the final volume,

b) the work if the pressure is 120 kPa

Answer 13

A 0.426 m3
B -8.88 kJ

Question 14

0 kg/s steam at 3 MPa, 300oC expands isentropically in a turbine to a pressure of 100 kPa. If the heat transfer from the casing to surrounding air represents 1 per cent of the overall change of enthalpy of the steam, calculate the power output of the turbine. Assume exit is 2 m above entry and that initial velocity of steam is 10 m/s whereas exit velocity is 1 m/s.

Answer 14

19

Question 15

A piston and cylinder mechanism contains 2 kg of a perfect gas. The gas expands reversibly and isothermally from a pressure of 10 bar and a temperature of 327  C to a pressure of 1.8 bar.

Calculate:

a) the work transfer,

b) the heat transfer; and

c) the specific change in enthalpy of the gas.

Take R=0.3 kJ/kg K and n=1.4

Answer 15

A 617 kJ
B 617 kJ
C 0

Question 16

The gas expanding in the combustion space of a reciprocating engine has an initial pressure of 50 bar and an initial temperature of 1623  C. The initial volume is 50000 mm 3 and the gas expands through a volume ratio of 20 according to the law pV 1 . 25 = constant. Calculate

a) the work transfer and

b) heat transfer in the expansion process.

Take R = 270 J/Kg K and C v = 800 J/Kg K.

Answer 16

A 527 J
B 136 J

Question 17

A reciprocating steam engine cylinder contains 2kg of steam at a pressure of 30 bar and a temperature of 300 C. The steam expands reversibly to a final pressure of 2 bar, according to the law pv 1. 2 = c Calculate

a) the final state of the stream,

b) the work transfer and

c) the heat transfer in the process.

Answer 17

A 0.875
B 884 kJ
C -63.4 kJ/kg

Question 18

Steam at a pressure of 6 MPa and a temperature of 500  C enters an adiabatic turbine with a velocity of 20 m/s and expands to a pressure of 50 kPa, and a dryness fraction of 0.98. The steam leaves with a velocity of 200 m/s. The turbine is required to develop 1MW. Determine:

a) the mass flow rate of steam required, when KE is neglected, and

b) What is the effect of KE on the answer?

Answer 18

A 2599.8kJ / kg
B 1.187 kg/s

Question 19

Air, which may be considered a perfect gas, enters an adiabatic nozzle with negligible velocity. The entry pressure is 6 bar and the exit pressure is 1 bar; the entry temperature is 760 K. The flow throughout the nozzle is reversible and the mass flow rate is 2 kg/s. Calculate the exit velocity.

Take Cp = 1004.5 J/kg K and n = 1.4

Answer 19

782m / s

Question 20

3 kg/s of steam enters an adiabatic condenser at a pressure of 100 kPa with dryness fraction 0.80,

and the condensate leaves the condenser at a temperature of 30 C. The condenser is cooled by

water which enters at a temperature of 5 C and leaves at a temperature of 25 C. Calculate the mass flow rate of cooling water required if all changes in kinetic and potential energy may be neglected. Assume Cp = 4.2 kJ/kgK, and the enthalpy at 100 kPa & 30oC = 125 kJ/kg.

Answer 20

75 kg / s

Question 21

A reciprocating compressor delivers 0.1 kg/s of air at a pressure of 12 bar. The air enters the compressor at a pressure of 1 bar and a temperature of 15 C. Calculate the delivery temperature of the air, the work transfer rate and the heat transfer rate in the compression process for:

i. reversible polytropic compression, PV 1 . 2 = constant;

ii. reversible adiabatic compression;

iii. reversible isothermal compression.

Answer 21

A −10.6kW
B 0
C 20.5kW

Question 22

A reciprocating internal combustion engine has a clearance volume of 0.0001m 3 and a compression ratio (volume ratio) of 10. The pressure and temperature of the combustion gases when the piston is at top dead centre are 4000 kN/m 2 and 1800ºC respectively.

Assuming that the expansion process follows PV 1.3 = constant, calculate:

a) the work transfer in this process, and

b) the temperature of the gases at the end of the process.

Answer 22

A 66.7 J
B 1039 K

Question 23

A reciprocating steam motor is supplied with dry saturated steam at a pressure of 1.6MPa ( specific volume = 0.1238 m3 /kg). The stroke of the motor is 0.8m and the bore is 0.3m. The clearance volume is negligible. The steam enters the cylinder, expands at constant pressure for ¼ of the stroke and then expands reversibly according to a law PV = constant, til the end of the stroke. Calculate

a) the mass of the steam,

b) the work transfer and the heat transfer in the process?

Answer 23

A 31.3 kJ
B 31.3 kJ

Question 24

A piston and cylinder mechanism has its piston fixed so that the volume contained is 0.0025m3 . The mechanism is filled with wet steam at a pressure of 2 bar. The steam is heated until it reaches the critical point. The piston is released and the steam expands adiabatically to a pressure of 2 bar and a volume of 0.5m3 . Calculate:

a) the mass of steam in the mechanism,

b) the dryness fraction of the steam after expansion.

Answer 24

A 0.788 kg
B 0.715

Question 25

A mass of gas occupying 0.08m 3 at 6kN/m 2 and 80°C is expanded reversibly in a non-flow process according to a law PV 1.2 = constant. The pressure at the end of expansion is 0.7kN/m2 . The gas is then heated at constant pressure to the original temperature. The specific heat capacities at constant pressure and constant volume are 1.00 and 0.74 kJ/kg K respectively. Determine:-

a) the work transfer in the expansion process;

b) the heat transfer in the expansion process;

c) the volume at the end of the heating process;

d) the change in internal energy during the heating process.

Answer 25

A 0.723 kJ
B -0.411 kJ

Question 26

An ideal centrifugal air compressor takes in air at 1 bar, 15ºC and compresses it reversibly and adiabatically to a pressure of 4 bar.

a) (Calculate the delivery temperature of the gas.

b) (If kinetic energy and potential energy changes are negligible calculate the specific work transfer in the compression process.

Air may be assumed to be a perfect gas with specific heat capacity at constant

pressure C p = 1.005kJ/kg K and n = 1.4.

Answer 26

A 428 K
B -140.7 kJ/kg

Question 27

A reversible adiabatic air turbine drives a small generator which requires a power of 2kW. The air supply for the turbine is provided by a reservoir and the pressure and temperature at turbine entry may be considered constant at 9 bar, 20ºC respectively. The velocity of the air at inlet to the turbine is small and may be neglected but at exit the velocity is 55m/s. The exit pressure is 1.2 bar. Calculate:

a) the air temperature at exit from the turbine, and

b) the mass flow rate of air stating any assumptions made.

Air may be considered a perfect as for which the specific heat capacity at constant pressure C p =

1.005 kJ/kg K and n = 1.4. A reversible adiabatic air turbine drives a small generator which requires a power of 2kW. The air supply for the turbine is provided by a reservoir and the pressure and temperature at turbine entry may be considered constant at 9 bar, 20ºC respectively. The velocity of the air at inlet to the turbine is small and may be neglected but at exit the velocity is 55m/s. The exit pressure is 1.2 bar. Calculate:

a) the air temperature at exit from the turbine, and

b) the mass flow rate of air stating any assumptions made.

Air may be considered a perfect as for which the specific heat capacity at constant pressure C p =

1.005 kJ/kg K and n = 1.4. A reversible adiabatic air turbine drives a small generator which requires a power of 2kW. The air supply for the turbine is provided by a reservoir and the pressure and temperature at turbine entry may be considered constant at 9 bar, 20ºC respectively. The velocity of the air at inlet to the turbine is small and may be neglected but at exit the velocity is 55m/s. The exit pressure is 1.2 bar. Calculate:

a) the air temperature at exit from the turbine, and

b) the mass flow rate of air stating any assumptions made.

Air may be considered a perfect as for which the specific heat capacity at constant pressure C p =

1.005 kJ/kg K and n = 1.4.

Answer 27

A 164.76 K
B 0.0157 kg/s

Question 28

Steam at a pressure of 2 MPa and a temperature of 240ºC enters a nozzle with a velocity of 15m/s. The steam expands reversibly and adiabatically in the nozzle to a pressure of 100 kPa and a dryness fraction of 0.9. Calculate the velocity of the steam at exit from the nozzle,

Answer 28

715 m/s

Question 29

A one pass steam generator receives saturated water at 20 bar, and converting it into steam at 400ºC. The mass flow rate of steam is 1200 kg/h, calculate the heat transfer in the generator.

Answer 29

149.667 kW

Question 30

1kg of gas occupies a volume of 0.4m 3 at a pressure of 100 kN/m2 . The gas is compressed isothermally to a pressure of 450 kN/m2 . Determine the work of compression, and the change in entropy of the gas during the compression. Assume for the gas R = 300 J/kgK

Answer 30

-60 kJ
-0.451 kJ/kgK

Question 31

A gas contained in a closed system at a pressure of 1 bar and temperature of 15ºC. A mass of 0.9kg of the gas is heated at constant pressure to raise its temperature from 15ºC to 250ºC. Determine the work done, and during the process. R = 0.185 kJ/kgK

Answer 31

39.1 kJ

Question 32

The cylinder of an engine has a stroke of 300mm and a bore of 250mm. The volume ratio of compression is 14:1. Air in the cylinder at the beginning of compression has a pressure of 96 kN/m 2 and a temperature of 93 ºC. The air is compressed for the full stroke according to the law PV 1.3 = C. Determine the work transfer per unit mass of air. Assume air R = 287 J/kgK.

Answer 32

-424 kJ/kg

Question 33

A mass of air at 330ºC, contained in a cylinder expanded polytropically to five times its initial volume and 1/8 th its initial pressure which is 1 bar. Calculate:

a) the value of the expansion index,

b) the work transfer per unit mass.

Answer 33

A 1.292
B 222 kJ

Question 34

Steam at a pressure of 10 bar and dryness fraction of 0.96 expands adiabatically to a pressure of 2 bar according to PV 1.12 = constant. Determine the work done during expansion per unit mass of steam.

Answer 34

246 kJ / kg

Question 35

A nuclear reactor generates 3000 MW of heat. The heat is transferred in a heat exchanger of energy transfer efficiency 75% into steam which is expanded in a turbine in order to produce a power output. The steam is condensed in a condenser, releasing 1800 MW of heat, and pumped back through the heat exchanger by a feed pump which requires 3% of the power output from the turbine. Determine:

a) The net power output from the plant.

b) The power output from the turbine.

c) The overall thermal efficiency of the plant.

Answer 35

A 463.9 MW
B 450 MW
C 15%

Question 36

Milk initially at 30ºC is to be kept in a chilled tank at 5ºC. If the total volume of milk is 100 litres, its density is 1100kg/m 3 and the specific heat capacity of 4.2kJ/kgK.

a) Determine the heat extraction rate assuming the chiller to be perfectly insulated

b) What would be the chiller consumption if heat transfer through the chiller body is?

i. + 5kW gain in summer, ii) -5kW loss in winter

Answer 36

A 11.55 kW
B 16.55 kW in summer
6.55 kW in winter

Question 37

Milk initially at 30ºC is to be kept in a chilled tank at 5ºC. If the total volume of milk is 100 litres, its density is 1100kg/m 3 and the specific heat capacity of 4.2kJ/kgK.

a) Determine the heat extraction rate assuming the chiller to be perfectly insulated

b) What would be the chiller consumption if heat transfer through the chiller body is?

i. + 5kW gain in summer, ii) -5kW loss in winter

Answer 37

A 11.55 kW
B 16.55 kW in summer
6.55 kW in winter

Question 38

You have a 200 gram cup of coffee at 100 C, too hot to drink.

a) How much will you cool it by adding 50 gm of water at 0 C?

b) How much will you cool it by adding 50 gm of ice at 0 C?

for ice assume h i = -333.5 and h f = 417 kJ/kgK

Answer 38

A 80C
B 64C

Question 39

Determine for a unit mass of air, the change in enthalpy when heated from zero C to 100O C if:

i. Cp = 1 kJ/kgK constant

ii.

Cp = 0.95 + 0.00002 * T – 0.03x10 -6xT2

Answer 39

A 100 kJ/kg
B 96.09 kJ / kg

Question 40

A burner heats air from 20 to 40oC at constant pressure. Determine the change in entropy for a unit mass of air going through the heater, assuming that for air Cp = 1 kJ/kgK

Answer 40

0.03356 kJ / kgK