6 Due 1/30

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? You do not have to compute this work, though a smart student could do it.

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 initially contains 5 L of R-134a at $-$10$\POW9,{\circ}$C. Because the piston is light and initially floats on the R-134a, the initial pressure inside the cylinder is the ambient 100 kPa one. However, if the volume would expand to 6 L, the piston would hit some stops and the volume could no longer increase any further. Now the cylinder is heated until the R-134a reaches 50$\POW9,{\circ}$C. Does the piston hit the stops? How do you know? What are the final pressure and volume? What is the work done by the R-134a in the process? Give a $Pv$ phase construction of the initial phase, drawing $P$ first. For the later phases 1a and 2, you can use your knowledge about the earlier phases to locate them. Show the process line as a thick line in the $Pv$ diagram. Also show the work graphically in the diagram.