# Homework Help: Reading a P-V Diagram for heat in/out and work in/out

1. Dec 17, 2011

### mm2424

1. The problem statement, all variables and given/known data
Predict whether heat is lost or gained by a gas, and whether work is done by the gas or the gas does work on its surroundings, given a P-V diagram.

2. Relevant equations

3. The attempt at a solution

I'm trying to understand how to read a P-V diagram and am wondering whether there are any shortcut ways of determining whether heat has been added to the gas (which I think is positive Q) or left the gas (which I think is negative Q), and whether the gas has done work (positive) or had work done to it (negative). Is it ok to say the following?

Adiabatic steps moving from left to right and downward on the diagram: 0 heat change and gas does (positive) work.

Adiabatic steps moving from right to left and upward on the diagram: 0 heat change and environment does work on gas (negative work).

Isovolumic step moving from bottom to top on the diagram: heat added to the gas (positive Q) and 0 W

Isovolumic step moving from top to bottom on the diagram: heat taken from the gas (negative Q) and 0 W

Isobaric step moving from left to right on the diagram: heat added to the gas (positive Q) and the gas does (positive) work.

Isobaric step moving from right to left on the diagram: heat taken from the gas (negative Q) and the environment does work on the gas (work is negative)

Isothermal step moving from left to right and downward on the diagram: heat added to the gas (negative Q) and the gas does (positive) work.

Isothermal step moving from right to left and upward on the diagram: heat taken from the gas (negative Q) and the gas does (negative) work.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 17, 2011

### Andrew Mason

Pretty good. I would make the following changes (in bold):

Adiabatic steps moving from left to right and downward on the diagram: 0 heat flow and gas does (positive) work: W = ΔU

Adiabatic steps moving from right to left and upward on the diagram: 0 heat flow and environment does work on gas (negative work):W = ΔU

Isovolumic step moving from bottom to top on the diagram: heat flow into the gas (positive Q) and 0 W: Q = ΔU

Isovolumic step moving from top to bottom on the diagram: heat flow out of the gas (negative Q) and 0 W: Q = ΔU

Isobaric step moving from left to right on the diagram: heat flow into the gas (positive Q) and the gas does (positive) work.

Isobaric step moving from right to left on the diagram: heat flow out of the gas (negative Q) and the environment does work on the gas (work is negative)

Isothermal step moving from left to right and downward on the diagram: heat flow into the gas (negative Q) and the gas does (positive) work: Q = W

Isothermal step moving from right to left and upward on the diagram: heat flow out of the gas (negative Q) and the gas does (negative) work: Q = W

AM