# Thermodynamics (work, pressure, volume)

## Homework Statement

A heat engine does work by using a gas at an initial pressure of 1000 Pa and volume .1m 3. Step-by-step, it then increases the pressure to 10,000 Pa (at constant volume), increases the volume to .15m3 (at constant pressure), decreases the pressure back to 1,000 Pa (at constant volume) and returns the volume back to .1m3 (at constant pressure).

1)How much work is done by the gas during the first step?

2)How much work is done by the gas during the second step?

3)How much work is done by this heat engine in one complete cycle?

4) What is the change in internal energy during the first step?

5)What is the change in internal energy during the second step?

6)What is the change in internal energy over one complete cycle?

7)How much heat is added to the gas in the first step?

8)How much heat is added to the gas in the second step?

9) How much heat is added to the gas in one complete cycle?

## Homework Equations

dW=P*dV
dU=Q-W

U=internal energy, Q= heat, w=work, p=pressure, v=volume

## The Attempt at a Solution

1) W = 0 J because volume is constant)
2)dW=P(dV) = 10000(.15-.1) = 500
3)third step dW=P(dV) = 1000(.15-.1) = 50 so I just did work=500-50=450???

4)-5) I'm not sure how to find Q so I can use the dU=Q-W equation. Is there another equation that I don't know about? I don't have enough information for Q = ((kAdT)t)/L
Any hints here??
6) I think it would be 0J because the internal energy is a state function and it starts and ends the same.

7)-9) will be a piece of cake once I get 4)-5)

ehild
Homework Helper
Nothing was given about the kind of the gas? Is it an ideal gas? If so, the internal energy is proportional to T: U=Cv* n* T where Cv is the specific heat capacity and n is the number of moles of the gas. For an ideal gas, Cv=f/2 R where f is the degrees of freedom of its molecules.

ehild

I suppose I can assume it is an ideal gas because all of the previous problems we have done have been dealing with ideal gases only. But even if it were implied, how would I find the number of moles of gas or the degree of freedom??

ehild
Homework Helper
You get n*R from the ideal gas law, and f=3 for mono-atomic gas molecules, 5 for two-atomic and 6 for three or more-atomic ones. Nothing was said about the kind of gas? Try f=5. The molecules of air, N2 and O2 are two-atomic. Or just give the result in terms of parameter f.

ehild