Practice Set
1.The connections of a reversible engine to three sources at 500 K, 400 K and
300 K are shown in Fig.. It draws 1500 kJ/min of energy from the source at 800
K and develops 200 kJ/min of work.
(i) Determine the heat interactions with the other two sources of heat.
(ii) Evaluate the entropy change due to each heat interaction with the engine.
(iii) Total entropy change during the cycle.
2. The specific heats of a gas vary linearly with absolute temperature according
to the following relations: cp = (0.85 + 0.00025 T) kg/kg K, and cv = (0.56 +
0.00025 T) kJ/kg K .If the entropy of the gas at 1 bar pressure and 273 K is
zero, find the entropy of the gas at 25 bar and 750 K temperature.
3. A closed system contains air at a pressure 1 bar, temperature 300 K and
volume 0.018 m3. This system undergoes a thermodynamic cycle consisting of
the following three processes in series: (i) Constant volume heat addition till
pressure becomes 5 bar, (ii) Constant pressure cooling, and (iii) Isothermal
heating to initial state. Represent the cycle on T-S and p-V plots and evaluate
the change in entropy for each process. Take cp = 0.718 kJ/kg K and R = 0.287
kJ/kg K.
4. An iron cube at temperature of 400 ℃ is dropped in an insulated bath having
10 kg water at 25 ℃ . The water finally reaches a temperature of 50 ℃ at
Steady state. If specific heat of water is equal to 4186 J/kg-K. Calculate the
entropy changes for iron cube and the water.
5.2 kg of water at 80 ℃ are mixed adiabatically with 3 kg of water at 30 ℃ in a
constant pressure process of 1 atm. Calculate The increase in the entropy of the
total mass of water due to the mixing process (cpof water =4.187 kJ/kg K.).
6.A vessel having a capacity of 0.05 m3 contains a mixture of saturated water
and saturated steam at a temperature of 245 ℃ The mass of the liquid present is
10 kg. Calculate
a.
b.
c.
d.
e.
f.
The pressure
The mass
The specific enthalpy
Specific volume
Specific entropy
Specific internal energy
Given at T =245℃, Psat=36.5 bar, Vf=0.001239 m3/kg, Vg=0.0546
m3/kg, hf=1061.4 kJ/kg, hfg=1740.2 kJ/kg K, Sf=2.74kJ/kg K,
Sfg=3.3585 kJ/kg K.
7.A piston-cylinder contains 3 kg of wet steam at 1.4 bar. The initial volume is
2.25 m3. The steam is heated until its temperature reaches 400 ℃. The piston is
free to move up or down unless it reaches the stops at the top. When the piston
is up against the stops, the cylinder volume is 4.65 m3. Determine the amount of
work and heat transfer to or from steam. Also, given
P (bar)
Ts(in ℃)
1.4
2
109.3
120.2
hf(in
kJ/Kg)
458.4
504.7
hfg(in kJ/Kg) hg(in kJ/kg) Vg(in m3/kg)
2231.9
2201.6
2609
2706
1.236
0.885
8. A steam is cycled between pressures 30 bar and 0.04 bar. Steam is dry
saturated at 30 bar. Other properties of steam are given as
P (bar) hf(in kJ/Kg) hg(in kJ/kg)
Sg(in kJ/kg-K)
Sf(in KJ/kg-K)
30
1008.3
2802.3
2.646
6.184
0.04
121.4
2554.5
0.423
8.476
Assume as carnot cycle,
a. Efficiency of the cycle
b. Steam consumption rate
c. Pump work
d. Assume Rankine cycle under the same condition and solve again for
part (a), (b) and (c).
9.A Rankine cycle operates between pressures of 80 bar and 0.1 bar. The
maximum cycle temperature is 600°C. If the steam turbine and condensate
pump efficiencies are 0.9 and 0.8 respectively, calculate the specific work and
thermal efficiency. Relevant steam table extract is given below.
10.The minimum pressure and temperature in an Otto cycle are 100 kPa and
27°C. The amount of heat added to the air per cycle is 1500 kJ/kg. (i) Determine
the pressures and temperatures at all points of the air standard Otto cycle. (ii)
Also calculate the specific work and thermal efficiency of the cycle for a
compression ratio of 8:1.
11.An engine equipped with a cylinder having a bore of 15 cm and a stroke of
45 cm operates on an Otto cycle. If the clearance volume is 2000 cm3 , compute
the air standard efficiency.
12. 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 temperature is
800°C. The turbine and compressor efficiencies are each 80%. Find (a) the
compressor work per kg of air, (b) the turbine work per kg of air, (c) the heat
supplied per kg of air, (d) the cycle efficiency, and (e) the turbine exhaust
temperature.
13.Helium is used as the working fluid in an ideal Brayton cycle. Gas enters the
compressor at 27°C and 20 bar and is discharged at 60 bar. The gas is heated to
l000°C before entering the turbine. The cooler returns the hot turbine exhaust to
the temperature of the compressor inlet. Determine: (a) the temperatures at the
end of compression and expansion, (b) the heat supplied, the heat rejected and
the net work per kg of He, and (c) the cycle efficiency and the heat rate. Take c p
= 5.1926 kJ/kg K.