# Work Done by Expanding Gas

1. Feb 12, 2015

### Mtscorpion12

1. The problem statement, all variables and given/known data

In a cylinder of an automobile engine, immediately after combustion the gas is confined to a volume of 50.0 cm3 and has an initial pressure of 3.00x106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy transfer by heat. (a) What is the final pressure of the gas? (b) How much work is done by the gas in expanding?
2. Relevant equations
For this problem, assume the gas in the engine is diatomic with γ = 1.40

3. The attempt at a solution
I have already solved part (a) of this problem, which is 2.44x106 Pa, but I am having a lot of trouble with part (b). I have found the equation W = -∫VfViPdv, but don't know exactly what to do with that. I know pressure is not a constant, so it can't be brought out of the integral. I'm really not sure where I should even start with this one.

2. Feb 12, 2015

### BiGyElLoWhAt

Anyway you can express pressure as a function of volume?

3. Feb 12, 2015

### BiGyElLoWhAt

Actually, can you determine the initial and final energies?

4. Feb 12, 2015

### Staff: Mentor

You know that PVγ = constant. This gives you enough information to perform the integration.

Chet

5. Feb 13, 2015

### BiGyElLoWhAt

True, but you also know that the gas is diatomic, which allows you to determine the energy at the initial state and final state. No need to integrate.

6. Feb 13, 2015

### Staff: Mentor

Yes. I agree. You can determine the relation between the initial and final temperatures in terms of the initial and final pressures , and then use ΔU =nCvΔT.

7. Feb 13, 2015

### Mtscorpion12

Thank you both for the help. I ended up setting P = constant/Vγ and integrating from there. I appreciate it.