# Homework #3 MEMS 0051 – Introduction to Thermodynamics solved

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Problem #1
A piston-cylinder device contains He gas initially at 150 [kPa], 20 ◦C and 0.5 [m3
]. The He gas is compressed in
a polytropic process to 400 [kPa] and 140 ◦C. Assume the He gas satisfies the ideal gas law. For He, R=2.0771
[kJ/kg-K], CP =5.2 [kJ/kg-K], C∀ =3.116 [kJ/kg-K]. Determine:
• The work into or out of the system during this process.
• The heat loss or gain during this process.
• Hint: Determine n.
Problem #2
Water contained in a piston-cylinder assembly undergoes two processes in series from an initial state where the
pressure is 1.0 [MPa] and the temperature is 400 ◦C. Process 1-2: The water is cooled as it is compressed at constant
pressure to the saturated vapor state at 1.0 [MPa]. Process 2-3: The water is cooled at constant volume to 150 ◦C.
• Sketch both processes on T-v and P-v diagrams in using the Matlab script previously developed.
• For the overall process determine the work, in [kJ/kg].
• For the overall process determine the heat transfer, in [kJ/kg].
Problem #3
A piston-cylinder device contains a 1.5 [kg] of water at a pressure of 200 [kPa] and a temperature of 150 ◦C. It
is heated in such a fashion that the pressure is linearly related to the volume, and reaches a final state where the
pressure is 600 [kPa] and the temperature is 350 ◦C.
• Find the final volume of the system and the work required for this process.
Problem #4
A piston-cylinder device with a set of stops in the middle initially contains 3 kg of air at 200 [kPa] and 500 K. The
air is compressed by lowering the frictionless piston in an isobaric process (n=0). When the piston hits the stops,
the gas volume is 50% of the initial volume. Assume air behaves as an ideal gas (R=0.287 [kJ/kg-K], CP =1.004
[kJ/kg-K], C∀ =0.717 [kJ/kg-K].
• If the final temperature is 300 K, determine the total work done on the system.
Problem #5
A piston-cylinder device contains 1.5 [kg] of air at a temperature of 300 K and a pressure of 150 [kPa]. It is heated
in a two-step process. The first step is a constant volume process where the final temperature is 1,000 K. The second
step is a constant pressure process where the final temperature is 1,500 K.
• Determine the final volume and work required for this two step process.
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