Minia University Mechatronics and Industrial Robotics Prog.

Faculty of Engineering
Mechanical Power Dept. Thermodynamics

SHEET (3)

1. Answer the following questions:

a. On a P-v diagram, what does the area under the process curve represent?
b. Is the boundary work associated with constant-volume systems always zero?
c. Show that 1 kPa · m3 = 1 kJ
d. In the relation u = m.cv.T, what is the correct unit of cv — kJ/kg · °C or kJ/kg · K?
e. A fixed mass of an ideal gas is heated from 50 to 80°C at a constant pressure of (a) 1
atm and (b) 3 atm. For which case do you think the energy required will be greater?
Why?
f. A fixed mass of an ideal gas is heated from 50 to 80°C (a) at constant volume and (b)
at constant pressure. For which case do you think the energy required will be greater?
Why?
g. Is it possible to compress an ideal gas isothermally in an adiabatic piston–cylinder
device? Explain.

2. A piston–cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 120°C.
The nitrogen is now expanded polytropically to a state of 100 kPa and 100°C. Determine
the boundary work done during this process.

3. A piston–cylinder device with a set of stops initially contains 0.3 kg of steam at 1.0 MPa
and 400°C. The location of the stops corresponds to 60 percent of the initial volume. Now
the steam is cooled. Determine the compression work if the final state is (a) 1.0 MPa and
250°C and (b) 500 kPa.(c) Also determine the temperature at the final state in part (b).

4. A piston–cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 120°C.
The nitrogen is now expanded to a pressure of 100 kPa polytropically with a polytropic
exponent whose value is equal to the specific heat ratio (called isentropic expansion).
Determine the final temperature and the boundary work done during this process.

5. A mass of 2.4 kg of air at 150 kPa and 12°C is contained in a gas-tight, frictionless
piston–cylinder device. The air is now compressed to a final pressure of 600 kPa. During
the process, heat is transferred from the air such that the temperature inside the cylinder
remains constant. Calculate the work input during this process.

6. A gas is compressed from an initial volume of 0.42 m3 to a final volume of 0.12 m3.
During the quasi-equilibrium process, the pressure changes with volume according to the
relation P = aV + b, where a = -1200 kPa/m3 and b = 600 kPa. Calculate the work done
during this process (a) by plotting the process on a P-V diagram and finding the area
under the process curve and (b) by performing the necessary integrations.

Thermodynamics –Sheet (3) Page 1 of 4

7. A piston–cylinder device contains 50 kg of water at 250 kPa and 25°C.
The cross-sectional area of the piston is 0.1 m2. Heat is now transferred
to the water, causing part of it to evaporate and expand. When the
volume reaches 0.2 m3, the piston reaches a linear spring whose spring
constant is 100 kN/m. More heat is transferred to the water until the
piston rises 20 cm more. Determine (a) the final pressure and temperature
and (b) the work done during this process. Also, show the process on a P-
V diagram.

8. A piston–cylinder device contains 0.15 kg of air initially at 2 MPa and 350°C. The air is
first expanded isothermally to 500 kPa, then compressed polytropically with a polytropic
exponent of 1.2 to the initial pressure, and finally compressed at the constant pressure to
the initial state. Determine the boundary work for each process and the net work of the
cycle.

9. A well-insulated rigid tank contains 5 kg of a saturated

liquid–vapor mixture of water at l00 kPa. Initially, three-
quarters of the mass is in the liquid phase. An electric
resistor placed in the tank is connected to a 220-V source,
and a current of 8 A flows through the resistor when the
switch is turned on. Determine how long it will take to
vaporize all the liquid in the tank. Also, show the process on
a T-v diagram with respect to saturation lines.

10. An insulated tank is divided into two parts by a partition.

One part of the tank contains 2.5 kg of compressed liquid water
at 60°C and 600 kPa while the other part is evacuated. The
partition is now removed, and the water expands to fill the entire
tank. Determine the final temperature of the water and the
volume of the tank for a final pressure of 10 kPa.

11. An insulated piston–cylinder device contains 5 L of

saturated liquid water at a constant pressure of 175 kPa.
Water is stirred by a paddle wheel while a current of 8 A
flows for 45 min through a resistor placed in the water. If
one-half of the liquid is evaporated during this constant-
pressure process and the paddle-wheel work amounts to 400
kJ, determine the voltage of the source. Also, show the
process on a P-v diagram with respect to saturation lines.

12. A piston–cylinder device initially contains steam at 200 kPa, 200°C, and 0.5 m3. At this
state, a linear spring (F α x) is touching the piston but exerts no force on it. Heat is now
slowly transferred to the steam, causing the pressure and the volume to rise to 500 kPa
and 0.6 m3, respectively. Show the process on a P-v diagram with respect to saturation
lines and determine (a) the final temperature, (b) the work done by the steam, and (c) the
total heat transferred.

13. A piston–cylinder device initially contains 0.8 m3 of saturated water vapor at 250 kPa. At
this state, the piston is resting on a set of stops, and the mass of the piston is such that a
pressure of 300 kPa is required to move it. Heat is now slowly transferred to the steam
until the volume doubles. Show the process on a P-v diagram with respect to saturation

Thermodynamics –Sheet (3) Page 2 of 4

 lines and determine (a) the final temperature, (b) the work done during this process, and
(c) the total heat transfer.

14. Two tanks (Tank A and Tank B) are separated

by a partition. Initially Tank A contains 2-kg
steam at 1 MPa and 300°C while Tank B
contains 3-kg saturated liquid–vapor mixture
with a vapor mass fraction of 50 percent. Now
the partition is removed and the two sides are
allowed to mix until the mechanical and thermal
equilibrium are established. If the pressure at
the final state is 300 kPa, determine (a) the
temperature and quality of the steam (if
mixture) at the final state and (b) the amount of
heat lost from the tanks.

15. A 4-m x 5-m x 7-m room is heated by the radiator of a

steam-heating system. The steam radiator transfers heat at a
rate of 10,000 kJ/h, and a 100-W fan is used to distribute
the warm air in the room. The rate of heat loss from the
room is estimated to be about 5000 kJ/h. If the initial
temperature of the room air is 10°C, determine how long it
will take for the air temperature to rise to 20°C. Assume
constant specific heats at room temperature.

16. A student living in a 4-m x 6-m x 6-m dormitory room turns on her 150-W fan before she
leaves the room on a summer day, hoping that the room will be cooler when she comes
back in the evening. Assuming all the doors and windows are tightly closed and
disregarding any heat transfer through the walls and the windows, determine the
temperature in the room when she comes back 10 h later. Use specific heat values at room
temperature, and assume the room to be at 100 kPa and 15°C in the morning when she
leaves.

17. An insulated rigid tank is divided into two equal parts by a partition. Initially, one part
contains 4 kg of an ideal gas at 800 kPa and 50°C, and the other part is evacuated. The
partition is now removed, and the gas expands into the entire tank. Determine the final
temperature and pressure in the tank.

18. A piston–cylinder device whose piston is resting on top of a set of stops initially contains
0.5 kg of helium gas at 100 kPa and 25°C. The mass of the piston is such that 500 kPa of
pressure is required to raise it. How much heat must be transferred to the helium before
the piston starts rising?.

19. A piston–cylinder device contains 0.8 kg of nitrogen initially at 100 kPa and 27°C. The
nitrogen is now compressed slowly in a polytropic process during which PV1.3 = constant
until the volume is reduced by one-half. Determine the work done and the heat transfer
for this process.

Thermodynamics –Sheet (3) Page 3 of 4

20. A piston–cylinder device contains 4 kg of argon at 250 kPa and 35°C. During a quasi-
equilibrium, isothermal expansion process, 15 kJ of boundary work is done by the system,
and 3 kJ of paddle-wheel work is done on the system. Determine the heat transfer for this
process.

21. A piston–cylinder device, whose piston is resting on a set of stops, initially contains 3 kg
of air at 200 kPa and 27°C. The mass of the piston is such that a pressure of 400 kPa is
required to move it. Heat is now transferred to the air until its volume doubles. Determine
the work done by the air and the total heat transferred to the air during this process. Also
show the process on a P-v diagram.

22. A piston–cylinder device, with a set of stops on the top, initially contains 3 kg of air at
200 kPa and 27°C. Heat is now transferred to the air, and the piston rises until it hits the
stops, at which point the volume is twice the initial volume. More heat is transferred until
the pressure inside the cylinder also doubles. Determine the work done and the amount of
heat transfer for this process. Also, show the process on a P-v diagram.

23. In a manufacturing facility, 5-cm-diameter brass

balls (ρ = 8522 kg/m3 and cp = 0.385 kJ/kg · °C)
initially at 120°C are quenched in a water bath at
50°C for a period of 2 min at a rate of 100 balls
per minute. If the temperature of the balls after
quenching is 74°C, determine the rate at which
heat needs to be removed from the water in order
to keep its temperature constant at 50°C.

24. Consider a 1000-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024-
T6 (ρ = 2770 kg/m3 and cp = 875 J/kg · °C). The base plate has a surface area of 0.03 m2.
Initially, the iron is in thermal equilibrium with the ambient air at 22°C. Assuming 85
percent of the heat generated in the resistance wires is transferred to the plate, determine
the minimum time needed for the plate temperature to reach 140°C.

25. An electronic device dissipating 30 W has a mass of 20 g and a specific heat of 850 J/kg ·
°C. The device is lightly used, and it is on for 5 min and then off for several hours, during
which it cools to the ambient temperature of 25°C. Determine the highest possible
temperature of the device at the end of the 5-min operating period. What would your
answer be if the device were attached to a 0.2-kg aluminum heat sink? Assume the device
and the heat sink to be nearly isothermal.

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