6 Due 2/3

1. A piston cylinder combination contains 2 kg of air at the ambient temperature of 25$\POW9,{\circ}$C and at the unknown ambient pressure. To provide a source of cooling on this hot Florida day, the piston is now pulled up until the air reaches a temperature of -100$\POW9,{\circ}$C. It can be assumed that the process is a polytropic one with $n=1.4$. What is the work that must be done on the air in the cylinder to pull up the piston and produce the cold air? The piston must also do work on the air outside the cylinder, which remains at the ambient pressure. What is the expression for that work?

2. Two cubic meters of a gas at 200 kPa expands polytropically with $n=5/3$ to standard atmospheric pressure. What is the work done by the gas in the process?

3. Air in a piston/cylinder combination with an initial volume of 1 m$\POW9,{3}$ is initially kept at a pressure of 150 kPa by the weight of the piston and the atmospheric pressure. It expands to 2 m$\POW9,{3}$, at which time the piston hits against a linear spring. The air then continues to expand to 4 m$\POW9,{3}$ while the pressure increases to 300 kPa due to the increasing spring force. Find the work done by the air in the complete process. Draw the $PV$ diagram very neatly and graphically show the two parts of the work done by the air.

4. A piston cylinder combination contains R-22 at $-30$$\POW9,{\circ}$C, 150 kPa, and 10 L. The R-22 is now heated to 15$\POW9,{\circ}$C. Initially the piston floats on the R-22. However, the cylinder has stops that limit the piston motion to a volume no larger than 11 L. Does the piston hit the stops? What is the work done by the R-22? You must construct the initial phase in the $Pv$ diagram. You can then find the other phases in the same diagram directly. Show the process as a fat line in the diagram, and show the work also graphically. Explain clearly in words why the possibility that the piston never hits the stop is wrong.