Course and Section_______ Names ___________________________

Date___________ _________________________________

A Heat Engine: The first and second laws of thermodynamics

We’ll make up a heat engine that consists of 4 steps, 2 at constant volume (isochoric) and 2 at constant pressure (isobaric). One mole of a monatomic ideal gas will undergo this cycle. This isn’t a realistic engine, but will illustrate the ideas of energy conservation and efficiency in a typical heat engine.

Here is what the cycle looks like on a P-V diagram.

Label the points a,b,c,d, starting at the upper left and going clockwise. The process is the following: The cycle starts at a; the gas first expands at constant pressure to point b (does heat enter or leave the gas during this process?________). Then its pressure is decreased at constant volume (how can this be accomplished?______________________). Then it is compressed at constant pressure. Finally, its pressure is increased at constant volume, returning the gas to its initial state.

1. Which of the processes ab,bc,cd,da are isochoric? Isobaric?

2. Given that we have just one mole of gas, find the temperatures at points a,b,c,d. Once you’ve found T_a, you can just use ratios to find the others. Fill in the table on the next page.

3. Now find the internal energies (U = 3/2 nRT = 3/2 PV) at each point a,b,c,d.

4. Find the work W = PDV done in each step of the cycle. Insert this into the second table on the next page.

5. Find the change in the internal energy, DU, for each step, and fill in that column of the table.

6. From the first law of thermodynamics, or from the heat capacities, find Q for each step of the cycle.

7. Finally, Find how much heat is taken in during one cycle, and how much net work is done by the gas. From this find the efficiency e = W_out /Q_in.

Point	T	U
a
b
c
d

Step	Q	W	DU
ab
bc
cd
da

e = ___________________