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Thermodynamics // Homework #2
Ideal Gas
Boundary Work and Polytropic Process
1.
A spherical balloon with a diameter of 6 m is filled with helium
11. A piston–cylinder device initially contains 0.07 m3 of nitrogen
at 20°C and 200 kPa. Determine the mole number and the mass
gas at 130 kPa and 120°C. The nitrogen is now expanded
of the helium in the balloon. {9.28 kmol, 37.15 kg}
polytropically to a state of 100 kPa and 100°C. Determine the
2.
3
The pressure gage on a 2.5-m oxygen tank reads 500 kPa.
Determine the amount of oxygen in the tank
if
3.
4.
the
temperature
is
28°C
and
12. A piston–cylinder device with a set of stops initially contains 0.3
the
kg of steam at 1.0 MPa and 400°C. The location of the stops
atmospheric pressure is 97 kPa. {19.08 kg}
corresponds to 60 percent of the initial volume. Now the steam
A rigid tank contains 20 lbm of air at 20 psia
is cooled. Determine the compression work if
and 70°F. More air is added to the tank until the pressure and
the final state is (a) 1.0 MPa and 250°C and
temperature rise to 35 psia and 90°F, respectively. Determine
(b) 500 kPa. (c) Also determine the
the amount of air added to the tank. {19.08 kg}
temperature at the final state in part (b).
A 400-L rigid tank contains 5 kg of air at 25°C. Determine the
{22.16 kJ, 36.79 kJ, 151.8ºC}
reading on the pressure gage if the atmospheric pressure is 97
kPa. {13.73 lbm}
5.
boundary work done during this process. {1.86 kJ}
13. A mass of 5 kg of saturated water vapor at 300 kPa is heated at
constant pressure until the temperature reaches 200°C. Calculate
3
A 1-m tank containing air at 25°C and 500 kPa is connected
the work done by the steam during this process. {165.9 kJ}
through a valve to another tank containing 5 kg of air at 35°C
14. A frictionless piston–cylinder device initially contains 200 L of
and 200 kPa. Now the valve is opened, and the entire system is
saturated liquid refrigerant-134a. The piston
allowed to reach thermal equilibrium with the surroundings,
is free to move, and its mass is such that it
which are at 20°C. Determine the volume of the second tank and
maintains a pressure of 900 kPa on the
3
the final equilibrium pressure of air. {2.2 m , 284 kPa.}
refrigerant. The refrigerant is now heated
Compressibility Factor
until its temperature rises to 70°C. Calculate
6.
Determine the specific volume of superheated water vapor at 10
the work done during this process. {5571
MPa and 400°C, using (a) the ideal-gas equation, (b) the
kJ}
generalized compressibility chart, and (c) the steam tables. Also
15. A frictionless piston–cylinder device contains 16 lbm of
determine the error involved in the first two cases. {0.03106
superheated water vapor at 40 psia and 600°F. Steam is now
3
7.
3
3
m /kg, 0.02609 m /kg, 0.02644 m /kg}
cooled at constant pressure until 70 percent of it, by mass,
Determine the specific volume of nitrogen gas at 10 MPa and
condenses. Determine the work done during this process.
150 K based on (a) the ideal-gas equation and (b) the
{1483 Btu}
generalized compressibility chart. Compare these results with
3
the experimental value of 0.002388 m /kg, and determine the
3
8.
3
25°C. The cross-sectional area of the piston is 0.1 m2. Heat is
error involved in each case. {0.004452 m /kg, 0.002404 m /kg}
now transferred to the water, causing part of it to evaporate and
Somebody claims that oxygen gas at 160 K and 3 MPa can be
expand. When the volume reaches 0.2 m3,
treated as an ideal gas with an error of less than 10 percent. Is
the piston reaches a linear spring whose
this claim valid? {false}
spring constant is 100 kN/m. More heat is
Specific Heat
9.
16. A piston–cylinder device contains 50 kg of water at 250 kPa and
transferred to the water until the piston
Determine the enthalpy change Δh of nitrogen, in kJ/kg, as it is
rises 20 cm more. Determine (a) the final
heated from 600 to 1000K, using (a) the empirical specific heat
pressure and temperature and (b) the work
equation as a function of temperature (Table A-2c), (b) the Cp
done during this process. Also, show the
value at the average temperature (Table A-2b), and (c) the Cp
process on a P-V diagram. {147.9 ºC,
value at room temperature (Table A-2a). {447.8 kJ/kg, 448.4
kJ/kg, 415.6 kJ/kg}
10. Determine the internal energy change Δu of the hydrogen, in
44.5kJ}
17. A piston/cylinder assembly contains 0.5 kg air at 500 kPa and
500 K.
The air expands in process such the P is linearly
kJ/kg, as it is heated from 400 to 1000K, (value at average
decreasing with volume to final state of 100 kPa, 300 K. Find
temperature). {6288 kJ/kg}
the work in the process. {86.1 kJ}
18. A piston/cylinder device contain 0.1 kg air at 100 kPa and 400 K
that goes through a polytropic compression process with n=1.3
to a pressure of 300 kPa. How much work has the air done in
the process? {11.04 kJ}
19. Nitrogen at initial state of 300 K, 150 kPa, and 0.2 m3 is
compressed slowly in an isothermal process to find pressure of
800 kPa. Determine the work done during this process. {50.2
kJ}
20. A cylinder fitted with a piston contains propane gas at 100 kPa
and 300K with a volume of 0.2 m3. The gas is now slowly
compressed according to the relation PV1.1 = constant a final
temperature of 340 K. Find the final pressure and the work done
during the process. {396 kPa, 26.7 kJ}
21. A piston/cylinder assembly contains butane, C4H10, at 300ºC and
100 kPa with a volume of 0.02 m3. The gas is now compressed
slowly in an isothermal process to 300 kPa. Determine the work
done by the butane during the process.
22. Air goes through a polytropic process from 125 kPa and 325 K
to 300 kPa and 500 K. Find the polytropic exponent n and the
specific work in the process.