Calculating Work Done by Expanding Gas in an Automobile Engine

[Mtscorpion12]

Homework Statement

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?

Homework Equations

For this problem, assume the gas in the engine is diatomic with γ = 1.40

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.

 

[BiGyElLoWhAt]

Anyway you can express pressure as a function of volume?

 

[BiGyElLoWhAt]

Actually, can you determine the initial and final energies?

 

[Chestermiller]

You know that PV^γ = constant. This gives you enough information to perform the integration.

Chet

 

[BiGyElLoWhAt]

You know that PV^γ = constant. This gives you enough information to perform the integration.

Chet

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.

 

[Chestermiller]

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.

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 =nC_vΔT.

 

[Mtscorpion12]

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