Is the Net Work Done Positive and Does It Function as a Heat Engine?

[groundhog92]

Homework Statement

A cylinder contains 2 moles of gas initially at state A it has a volume of 1*10^-2m^3 and a pressure of 4*10^5. It the is brought isobarically to state B where the new volume is 2*10^-2. It is then brought at a constant volume to state C where the temperature is the same as in step A. It is then finally brought isothermally back to state A.
a)Is the net work done during the complete cycle positive, negative, or zero?
b)Is this device a heat engine or a refrigerator?

Homework Equations

Work=p(V2-V1)

The Attempt at a Solution

I've already got answers but I'm not positive.

Part a
Positive b/c the work done by the gas going from A to B is greater than the work done on the gas going from C to A. This is seen through A bring at a higher pressure than C while they have the same differential in volume. No work is done from B to C.

Part b
I said it is a heat engine for two reasons. First the heat of the system increases and second b/c the work done during the cycle is positive. In a refrigerator work more work must be done on the system for the cold air to move to the hot region.

 

[bucher]

Everything seems to check out here.

You should probably make a P-V graph if you want to show your answers better.

 

[nlightner]

Your attempt at a solution seems correct. The net work done during the cycle is positive because the work done from A to B is greater than the work done from C to A. This means that the system is able to perform work on its surroundings during the cycle.

As for part b, you are correct in saying that it is a heat engine. In a refrigerator, work is done on the system to move heat from a cold region to a hot region. In this problem, work is done by the system to move heat from a hot region to a cold region, which is the definition of a heat engine. Additionally, the fact that the heat of the system increases during the cycle also supports this conclusion.