I. Part I

Let v = volume inside flask, s = volume inside syringe

(Vsys)(P) = k

(v + s)(P) = k

s = k/P – v

v = y-intercept = 151.7 mL

II. Part II, four process cycle

Graphs:

Pressure vs. Volume

Questions:

1.

2. The area under the curve represents work done on the system. In process 2, work is negative because the volume of the gas increases. In process 4, work is positive because the volume of the gas decreases.

3. The internal energy during the isothermal processes must remain constant because temperature does not change (and internal energy is directly proportional to temperature). This is achieved through a heat gain or loss that balances the energy gained or lost through work (i.e. if work was done on the gas, the gas would lose heat).

4.

W_net = –291 mL-kPa = –.291 J

III. Part 2, three-process cycle

1.

2. The syringe would have to be compressed incrementally—i.e. wait until the gas cools enough so that its pressure begins to drop, then compress it a little bit until the pressure goes back up. Repeat until the system returns to its original volume.

IV. Extensions

1. The work done on the gas is positive. For the two isothermal processes, the change in volume is the same, but the expansion is done at a lower temperature and therefore a lower pressure. Since work is proportional to pressure, the magnitude of the work done during the expansion phase (corresponding to negative work) will be less than the magnitude during the compression phase (corresponding to positive work), and the net work will be positive.

2.

The Carnot cycle differs in that the process we went through was not ideal. There was energy loss (e.g. due to friction), and so less of the heat input was converted to work in our engine than would be in a Carnot engine.