Hi,

I'm just starting to learn thermodynamics and I'm completely stuck with a problem:

A stationary vertical cylinder, closed at the top, contains a gas whose volume may be changed with the aid of a heavy, frictionless piston of weight w.

a) How much work is done by the external force in compressing the gas by an amount dV by raising the piston a distance dy?

b) If this device is used as part of an engine, what expression is appropriate to calculate the net work delivered to or received from the surroundings?

c) If this device is used only to produce temperature changes of the gas, what expression for work would be appropriate?

Ok, if I'm not wrong that would be classified as a typical hydrostatic system with thermodynamic coordinates P, V and T. And it should be a quasi-static process. Can I assume that the gas is an ideal gas and that the process would be isothermal? So that $\displaystyle W=\int_{V_{i}}^{V_{f}} P dV$?

Then, by getting a free body diagram, I could work out P?

For question b, I assume that it would have to be the net work done during a cycle. Which would be the combination of compression and expansion.

And for question c, I think it should be an isobaric process? So that the Volume and the temperature change but the pressure stays constant?

Are these assumptions and ideas correct and how could I formalize them to answer the questions properly?

Thanks a lot!