Sana'a University
Thermodynamics I
Faculty of Engineering 2009-2010
Mechanical Engineering Department 3rd Year
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Sheet No. 2
Heat and Work
1. The volume of air changes from 100 liters to 250 liters when it expands under a
constant pressure of 10 bar. Draw the pressure- volume diagram for the process and
determine the work done during the process.
2. Determine the work done when the pressure of a gas in a rigid cylinder of volume 0.15
m3 is increased from 1.5 bar to 5 bar, Draw the P-V diagram for the process.
3. Air at a pressure of 1 bar and volume 0.6 m3 is compressed to a volume of 0.2 m3 is
such a way that PV = constant. Find the work done on the system during the process
and the final pressure.
4. A gas expands in a cylinder from a volume of 0.18 m 3 and a pressure of 5 kgf/cm2 to a
volume of 0.36 m3 according to the law PV1.2= C. Calculate the final pressure and the
work done.
5. A gas expands in a closed system when the pressure changes according to the equation
P= 20V + 15 bar; V is in m3. During the process the volume changes from 0.2 m3 to 0.6
m3. Calculate the work done during the process.
6. A spherical balloon of radius 10 cm contains air at a pressure of 1.5 kg f/cm2. When the
balloon is left exposed in the sun for some time, its radius is found to increase by 1 cm,
assuming that the pressure in the balloon is directly proportional to its radius,
determine:
a- The index of expansion,
b- The final pressure of the balloon, and
c- The work done by the system during the process.
7. In a piston-cylinder arrangement 1 kg of air at a pressure of 1 kg f/cm2 and volume of
0.2 m3 expands under constant pressure to a volume of 0.8 m 3; it then under goes a
constant volume process is such a manner that a change in the air pressure has been
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occurred after which the air is compressed according to the law PV = constant until the
air returns to its initial state. Represent the cycle on the diagram and determine the net
work done by the system.
8. A piston cylinder device contains 0.05 m 3 of a gas initially at 200 kPa at this state, a
linear spring that has a spring constant of 150 kN/m is touching the piston but exerting
no force on it. Now heat is transferred to the gas causing the piston to rise and to
compress the spring until the volume inside the cylinder doubles. If the cross sectional
area of the cylinder is 0.25 m2 determine:
a- The final pressure inside the cylinder,
b- The total work done by the gas and
c- The fraction of this work done against the sprig to compress it also find the
work exerted against the piston weight.
9. A storage battery is well insulated (thermally) while it is being charged. The charging
voltage is 12.3 V (volts) and the current is 24 A (amperes). Considering the storage
battery as the system, what are the heat transfer and work in 15-minute period?
10. A cylinder fitted with a frictionless piston contains 8 kg of superheated refrigerant R-
134a at 400 kPa and 100 ºC. The setup is cooled at constant pressure until the
refrigerant reaches a quality of 25 %. Calculate the work done in the process.
11. A balloon behaves such that the pressure inside is proportional to the diameter squared.
It contains 2 kg of R-134a at 0 ºC and 60 % quality. The balloon and R-134aq are now
heated so that a final pressure of 600 kPa is reached. Considering the R-134a as a
control mass, find the amount of work done in the process. Note that, P d2, V d3,
or P V2/3.
12. The refrigerant R-134a is contained in a piston-cylinder as shown in Fig. (1). Where
the volume is 11 L when the piston hits the stops. The initial state is -10 ºC and 180
kPa with a volume of 8 L. This system is brought indoor and warms up to 20 ºC. a) Is
the piston at the stops in the final state? b) Find the work done by the R-134a during
this process.
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13. A piston-cylinder device contains 50 kg of water at 150 kPa and 25 ºC as Fig. (2). The
cross-section 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 m 3, 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.
Fig.(1) Fig.(2)
