8 Due 10/8

1. Hot 500$\POW9,{\circ}$C copper with a volume of 2 L is dumped in 200 L light oil initially at 20$\POW9,{\circ}$C. Assuming no heat transfer with the surroundings, what is the final temperature?

2. Carbon dioxide changes in temperature from 500 to 1300 K. Find the change in specific internal energy
   1. using a constant $C_v$ from table A.5
   2. using the $C_v$ evaluated from equation in A.6 at the average temperature.
   3. Using the values listed in table A.8

3. Air is kept inside a cylinder by a piston constrained by a linear spring. Initially there is 3 kg of air at 300 K and 160 kPa. It is then heated to 900 K to a final volume of twice the initial volume. Plot the process in a $Pv$ diagram. Find the work done by the substance and heat added.

4. In an ideal diesel cycle, the combustion is assumed to be isobaric. The working fluid is assumed to be air. Assume that at the start of the combustion the temperature is 1000 K, the pressure 7 MPa, and that 1800 kJ/kg of heat is added.
   • What is the final temperature, and the work done by the air?
   • What are these same quantities if you use table A.5 values only?