9 Due 2/18

1. A steel tank contains 2 kg of carbon dioxide gas at 100 kPa, 1000 K that is heated to 1400 K. Find the heat transfer using
   1. the heat capacity from Table A-2(a);
   2. the heat capacity at 1000 K from Table A-2(b);
   3. the heat capacity at the average temperature from Table A-2(c);
   4. the ideal gas properties from Table A-20.
   Comment on the accuracy of the first three methods.

2. An 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 $P$.

3. 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.

4. 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$\POW9,{3}$/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?