Question bank:
1. A system receives 42 kJ of heat while expanding with volume change of 0.123 m3 against an
atmosphere of
12 N/cm2. A mass of 80 kg in the surroundings is also lifted through a distance of 6 metres.
(i)
Find the change in energy of the system.
(ii)
The system is returned to its initial volume by an adiabatic process which requires 100 kJ of
work. Find the change in energy of system.
(iii)
Determine the total change in energy of the system.
[Ans. (i) 22.54 kJ, (ii) 100 kJ, (iii) 122.54 kJ]
2. A tank contains 2.26 m3 of air at a pressure of 24.12 bar. If air is cooled until its pressure and
temperature becomes 13.78 bar and 21.1°C respectively. Determine the decrease of internal energy.
[– 5857.36 kJ]
3. Determine work done by fluid in the thermodynamic cycle comprising of following processes :
(a) Unit mass of fluid at 20 atm and 0.04 m3 is expanded by the law PV1.5 = constant, till volume gets
doubled.
(b) Fluid is cooled isobarically to its original volume.
(c) Heat is added to fluid till its pressure reaches to its original pressure, isochorically.
[18.8 kJ]
4. Air at 8 bar, 100°C flows in a duct of 15 cm diameter at rate of 150 kg/min. It is then throttled by a
valve upto 4 bar pressure. Determine the velocity of air after throttling and also show that enthalpy
remains constant before and after throttling.
[37.8 m/s]
5. Determine the power required by a compressor designed to compress atmospheric air (at 1 bar,
20°C)
to 10 bar pressure. Air enters compressor through inlet area of 90cm2 with velocity of 50 m/s and
leaves with velocity of 120 m/s from exit area of 5 cm2. Consider heat losses to environment to be 10%
of power input to
compressor.
[50.4 kW]
6. A frictionless piston is free to move in a closed cylinder. Initially there is 0.035 m3 of oxygen at 4.5
bar, 60°C on one side of the piston and 0.07 m3 of methane at 4.5 bar and – 12°C on the other side. The
cylinder walls and piston may be regarded as perfect thermal insulators but the oxygen may be heated
electrically. Heating takes place so that the volume of oxygen doubles. Find :
(i)
Final state condition ; (ii) Work done by the piston ;
(ii)
Heat transferred to oxygen.
Treat both gases as perfect and take :
For oxygen cp = 0.88 kJ/kg K, R = 0.24 kJ/kg K
For methane cp = 1.92 kJ/kg K, R = 0.496 kJ/kg K.
7. The specific heat at constant pressure of one kg fluid undergoing a non-flow constant pressure
process is
given by
where T is in °C.
The pressure during the process is maintained at 2 bar and volume changes from 1 m3 to 1.8 m3
and temperature changes from 50°C to 450°C.
Determine :
(i) Heat added (ii) Work done
(iii) Change in internal energy (iv) Change in enthalpy.
8. The resistance of the winding in a certain motor is found to be 75 ohms at room (25oC). When
operating at full load under steady state conditions, the motor is switched off and the resistance of the
winding s is immediately measured again, and found to be 90 ohms. The windings are made of copper
whose resistance at temperature toC id given by Rt = Ro [1+0.00393t] where R0 is the resistance at 00C.
Find the temperature of the coil during full load
9. A certain working fluid undergoes a process in such a way that pressure and volume are related as ,
Where p is in kPa and V is in m3 . During the process the volume changes from 0.15 m3 to 0.1 m3.
Determine the work done in the process.
10. A gas occupies 0.3m3 at 2 bar. It undergoes a cycle consisting of the following processes a)1-2
constant pressure process with work interaction of 15kJ b)2-3 constant temperature process and E3=E2
c) 3-1 constant volume and change in internal energy E1-E3 is-40kJ. Determine network and net heat
transfer for the cycle.
11. A piston-cylinder assembly contains 1kg or nitrogen at 100 kPa. The initial volume is 0.5 m3. Heat is
transferred to the substance in an amount necessary to cause a slow expansion at constant
temperature. This process is terminated when the final volume is twice the initial volume. Estimate the
amount of heat transferred.[Molecular wt. 28 & Cv=0.773 kJ/kgK]
12. 0.115m3 of gas has a pressure of 138 kN /m2. It is compressed to 680 kN /m2according to the law
PV1.4 =C, Determine the volume of the gas, work done and heat transferred.
13. The gas is compressed from initial state of 0.35 m3 and 105 kPa to a final state of 0.14 m3 and to
the same pressure .Determine the change in internal energy of the gas which transfers 38 kJ of heat.
14. A piston and cylinder device contains 1 kg of air, Initially, v = 0.8 m3/kg and
T = 298 K. The air is compressed in a slow frictionless process to a specific volume of 0.2 m3/kg and a
temperature of 580 K according to the equation pV1.3 = 0.75 ( p in bar, v in m3/kg). If Cv of air is 0.78
kJ/kg determine :
work and
heat transfer (both in kJ)
15. A piston-cylinder assembly contains 1kg or nitrogen at 100 kPa. The initial volume is 0.5 m3. Heat is
transferred to the substance in an amount necessary to cause a slow expansion at constant
temperature. This process is terminated when the final volume is twice the initial volume. Estimate the
amount of heat transferred.[Molecular wt. 28 & Cv=0.773 kJ/kgK](16)
16. A closed system undergoes a cycle consisting of three process 1-2, 2-3 and 3-1. Given that Q12 = 30
kJ, Q23 = 10 kJ, 1w2 = 5 kJ, 3w2 = 5 kJ and DE31 = 15 kJ, determine Q31, w23, DE12 and DE23.
17. The following cycle involves 3 kg of air : Polytropic compression from 1 to 2 where P1 = 150 kPa, T1
= 360 K, P2 = 750 kPa and n = 1.1 ; constant-pressure cooling from 2 to 3; and constant - temperature
heating from 3 to 1. Draw the pV diagram and find temperatures, pressures and volumes at each state
and determine the net work and heat.
18. A reversible engine is operating between 1000 K and 300 K. Find the efficiency of the engine. Also
find the power developed, in kW if the amount of heat received from high temperature reservoir is 500
kJ per min.
19. A refrigerator operating on reversible cycle is pumping heat from -5oC to the atmosphere at 40oC.
If it has to pump 24000 kJ/hr, find the power required to run the refrigerator.
20. Calculate the power developed and diameter of the inlet pipe, if air enters at 5 kg/s, 50m/s with an
enthalpy of 0.9 MJ/kg and leaves at 150 m/s with an enthalpy of 0.4 MJ/kg. The heat loss to the
surroundings is 0.025MJ/kg. Assume 100kPa and 300 K at the inlet
21. In an isentropic flow through nozzle, air flow at the rate of 600 kg/hr. At inlet to
the nozzle, pressure is 2MPa and temperature is 127oC. The exit pressure is 0.5
MPa. Initial air velocity is 300 m/s determine exit velocity of air, inlet and exit
area of nozzle.
22. Two heat engines operating on carnot cycle are arranged in series. The engine A
receives heat at 1000 K and rejects heat at a constant temperature T2. The engine
B receives heat rejected by A, and in turn rejects heat to a reservoir at 300 K.
Calculate the T2 when a) the efficiency of the two engines are equal b) the work
output of the two engines are equal.
23. A carnot engine receives 90kJ from a reservoir at 900 K. It rejects heat to he
environment at 300 K. One-fifth of its work output is used to drive a carnot
refrigerator. The refrigerator rejects 60 kJ to the environment at 300 K. Find work
output and efficiency of the engine, the temperature of the sink for the refrigerator in
degree celsius.
24. Three reversible engines of Carnot type are operating in series between the limiting temperatures
of 1100 K and 300 K. Determine the intermediate temperatures if the work output from engines is in
proportion of 3 : 2 : 1.
25. In a compressor the air enters at 27°C and 1 atm and leaves at 227°C and 1 MPa. Determine the
work done per unit mass of air assuming velocities at entry and exit to be negligible. Also determine the
additional work required, if velocities are 10 m/s and 50 m/s at inlet and exit
respectively.
26. In a gas turbine installation air is heated inside heat exchanger upto 750°C from ambient
temperature of 27°C. Hot air then enters into gas turbine with the velocity of 50 m/s and leaves at
600°C. Air leaving turbine enters a nozzle at 60 m/s velocity and leaves nozzle at temperature of 500°C.
For unit mass flow rate of air determine the following assuming adiabatic expansion in turbine and
nozzle,
(i)
heat transfer to air in heat exchanger
(ii)
power output from turbine
(iii)
velocity at exit of nozzle.
Take cp for air as 1.005 kJ/kg°K.
27. A refrigerator operates on reversed Carnot cycle. Determine the power required to drive
refrigerator between temperatures of 42ºC and 4ºC if heat at the rate of 2 kJ/s is extracted from the low
temperature region.
28. A piston and cylinder machine containing a fluid system has a stirring device as shown in Fig. 1.1 The
piston is frictionless, and it is held down against the fluid due to atmospheric pressure of 101.3 kPa. The
stirring device is turned 9500 revolutions with an average torque against the fluid of 1.25 Nm.
Meanwhile the piston of 0.65 m diameter moves out 0.6 m. Find the net work transfer for the
system.
Fig. 1.1
29. At the inlet to a certain nozzle the enthalpy of fluid passing is 2800 kJ/kg, and the velocity is 50 m/s.
At the discharge end the enthalpy is 2600 kJ/kg. The nozzle is horizontal and there is negligible heat loss
from it.
a.
Find the velocity at exit of the nozzle.
b. If the inlet area is 900 cm2 and the specific volume at inlet is 0.187 m3/kg, find the mass flow rate.
c.
If the specific volume at the nozzle exit is 0.498 m3/kg, find the exit area of nozzle. [8]
30. A fluid system, contained in a piston and cylinder machine, passes through a complete cycle of four
processes. The sum of all heat transferred during a cycle is – 340 kJ. The system completes 200 cycles
per min. Complete the following table showing the method for each item, and compute the net rate of
work output in kW.
[8]
Process
Q (kJ/min)
W (kJ/min)
ΔE (kJ/min)
1—2
2—3
3—4
0
42000
–4200
4—1
4340
0
—
—
—
—
– 73200
—
___
31. During flight, the air speed of a turbojet engine is 250 m/s. Ambient air temperature is – 14°C. Gas
temperature at outlet of nozzle is 610°C. Corresponding enthalpy values for air and gas are respectively
250 and 900 kJ/kg. Fuel air ratio is 0.0180. Chemical energy of fuel is 45 MJ/kg. Owing to incomplete
combustion 6% of chemical energy is not released in the reaction. Heat loss from the engine is 21 kJ/kg
of air. Calculate the velocity of the exhaust jet.
[8]
32. The connections of a reversible engine to three sources at 500 K, 400 K and 300 K are shown in Fig.
1.3. It draws 1500 kJ/min of energy from the source at 500 K and develops 200 kJ/min of work.
a.
Determine the heat interactions with the other two sources of heat.
b. Evaluate the entropy change due to each heat interaction with the engine.
c.
Total entropy change during the cycle.
[8]
33. 3 kg of water at 80°C is mixed with 4 kg of water at 15°C in an isolated system. Calculate the change
of entropy due to mixing process.
34. Two tanks A and B contain 1 kg of air at 1 bar, 50ºC and 3 bar, 50ºC when atmosphere is at 1
bar,15ºC. Identify the tank in which stored energy is more. Also find the availability of air in each
tank.
35. A cold storage plant of 40 tonnes of refrigeration capacity runs with its performance just
1/4 th of itsCarnot COP. Inside temperature is –15ºC and atmospheric temperature is 35ºC.
Determine the powerrequired to run the plant. [Take : One ton of refrigeration as 3.52 kW]
36. A vessel of volume 0.2 m3 has 2 kg of water at 200 o C find p, h and x
37. In a power station, the saturated steam is generated at 200ºC by transferring the heat from hot
gases in a steam boiler. Find the increase in total entropy of the combined system of gas and water and
increase in unavailable energy due to irreversible heat transfer. The gases are cooled from 1000°C to
500°C and all the heat from gases goes to water. Assume water enters the boiler at saturated condition
and leaves as saturated steam
38. One kg of air is compressed polytropically from 1 bar pressure and temperature of 300 K to a
pressure of 6.8 bar and temperature of 370 K. Determine the irreversibility if the sink temperature is 293
K. Assume R = 0.287 kJ/kg K, cp = 1.004 kJ/kg K and cv = 0.716 kJ/kg K.
39. water is heated from 40oC in a piston cylinder arrangement until it becomes s aturated
vapour at a constant pressure of 50 bar. Find the heat to added per kg.
40. A steam power plant works between 40 bar and 0.05 bar. If the steam supplied is dry saturated and
the cycle of operation is Rankine, find : (i) Cycle efficiency (ii) Specific steam consumption.
41. In a regenerative cycle the inlet conditions are 40 bar and 400°C. Steam is bled at 10 bar in
Regenerative heating. The exit pressure is 0.8 bar. Neglecting pump work determine the efficiency of
the cycle.
42. A steam power plant operates on ideal Rankine cycle using reheater and regenerative feed water
heaters. It has one open feed heater. Steam is supplied at 150 bar and 600°C.The condenser pressure is
0.1 bar. Some steam is extracted from the turbine at 40 bar for closed feed water heater and remaining
steam is reduced at 40 bar to 600°C. Extracted steam is completely condensed in this closed feed water
heater and is pumped to 150 bar before mixing with the feed water heater. Steam for the open feed
water heater is bled from L.P. turbine at 5 bar. Determine :
(i) Fraction of steam extracted from the turbines at each bled heater, and
(ii) Thermal efficiency of the system.
Draw the line diagram of the components and represent the cycle on T-s diagram.
43. The atmospheric conditions are 30ºC and specific humidity of 0.0215 kg/kg of air. Determine :
(i)
Partial pressure of air
(ii)
Relative humidity
(iii) Dew point temperature.
Atmospheric pressure = 756 mm Hg.
44. 1 kg of air at 24ºC and a relative humidity of 70% is to be mixed adiabatically in a steady state,
steady flow device with 1 kg of air at 16ºC and a relative humidity of 10%. Assuming that the mixing is to
be carried out at a constant pressure of 1.0 atm, determine the temperature and relative humidity of
the stream leaving the device.
45. In a laboratory test, a psychrometer recorded 36ºC DBT and 30ºC WBT. Calculate :
(i)
Vapour pressure
(ii)
Relative humidity
(iii)
Specific humidity
(iv)
Degree of saturation
(v)
Dew point temperature
(vi)
Enthalpy of the mixture.
46. An air-water vapour mixture enters an adiabatic saturator at 30ºC and leaves at 20ºC, which is the
adiabatic saturation temperature. The pressure remains constant at 1 bar. Determine the relative
humidity and the humidity ratio of the inlet mixture.
47. The following observation were made during a testing of moist air
Dry bulb temperature Tdb
=
29oC
Dew point temperature Tdb =
15oC
Total pressure
=
1 bar
Determine the relative humidity and degree of saturation
48
In a combined heating and humidification process, moist air enters heating coil with the dry bulb
temperature 20oC and 30% R.M. After the process the drug bulb temperature and the RH of Air were
found to be 40oC and 55% RH. The air passes through the heating at the rate of 350 kg/min
49 In an air conditioning plant, fresh air is used to mix up with returned air from conditioned space.
The fresh air drawn from atmosphere has the drug bulb temperature 32oC and we bulb temperature
25oC. The fresh air is drawn at the rate of 100m3/min. The returned air from conditioned space has the
drug bulb temperature 23oC and relative humidity 50%. The volume flow rate of it 540 m3/min.
Determine the (i) dry bulb and web bulb temperature (ii) specific humidity of mixture
50
Find the value of co-efficient of volume expansion β and isothermal compressibility K for a Van
der Waals’ gas obeying