9 Due 10/9

1. Air in a piston/cylinder combination is being heated at a rate of 50 kW. At a certain time, the temperature is 25$\POW9,{\circ}$C, the pressure 200 kPa, the volume 2 m$\POW9,{3}$ and the rate of volume change $\dot V$ is 0.2 m$^3$/s. What is the power produced by the air and what is the rate of change in temperature in $\POW9,{\circ}$C/s at that time?

2. A piston/cylinder contains helium at 500 K and 1200 kPa. It expands polytropically with $n=1.667$ to a pressure of 100 kPa. Find the final temperature, the specific work and specific heat transfer in the process.

3. Part of a Stirling engine cycle is an isochoric heat addition. Assume that the substance is 2kg of air and the pressure and temperature before the heat addition are 1000 kPa and 27$\POW9,{\circ}$C. The pressure is raised to 3000 kPa. Find the heat transfer using
   1. properties from Table A.7.1
   2. the heat capacity from Table A.5

4. A insulated steel tank is divided into two parts of 3 m$\POW9,{3}$ each by an initially locked piston. Side A has air at 200 kPa, 300 K, and side B has air at 1.0 MPa, 1000 K. The piston is now unlocked so it is free to move, and it conducts heat so the air comes to a uniform temperature $T_A=T_B$. Find the mass in both A and B, and the final $T$ and $P$.