# Thermodynamics problem! How to find the temperature of a gas.

1. Dec 8, 2011

### UCstudent

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

In an engine, 0.45 moles of gas at 1050 degrees K in a cylinder expand adiabatically against the piston. The gas does 3200 J of work against the piston. What is the final temperature of the gas?

2. Relevant equations

What formula do I use?

3. The attempt at a solution

The only formula I can think to use is

W=(-P)(delta V)

But pressure and volume aren't given, and I can't find them with the given information.

2. Dec 8, 2011

### ehild

Assume that the gas is ideal and apply the ideal gas law together with the First Law of Thermodynamics.

ehild

3. Dec 8, 2011

### UCstudent

How do you apply the first law of thermodynamics?

4. Dec 9, 2011

### Andrew Mason

First law: Q = ΔU + W where W = work done by the gas.

Here you are given Q and W. You first have to determine ΔU.

In order to find the change in temperature, however, you have to know the relationship between ΔU and ΔT. That depends on the gas. Are you given the Cv of the gas?

AM

5. Dec 9, 2011

### ehild

What have you learnt about adiabatic expansion of a gas? What is the relation among pressure and volume during such a process?
Anyway, you need to know the ratio Cp/Cv. You do not need the initial volume and pressure to solve the problem.
Collect all equations you know and are relevant: The ideal gas law, the adiabatic equation of state (you can derive it using the First Law if you do not know it) and the expression of work done by the gas.

ehild

6. Dec 9, 2011

### Andrew Mason

I don't think the adiabatic condition applies here since there is no indication that it is a quasi-static adiabatic expansion. Besides, one would need to know either P or V as well as T. However, we do need to know Cv to solve the problem

AM

7. Dec 9, 2011

### ehild

You are right, we do not need to assume a quasi static process. But we need to know if it is an ideal gas and the number of atoms in its molecules, or Cv for the internal energy. .

ehild

8. Dec 9, 2011

### netgypsy

Sounds like you have to assume ideal gas

9. Dec 12, 2011

### UCstudent

10. Dec 12, 2011

### netgypsy

No problem - guess you got it :-)

11. Dec 12, 2011

### UCstudent

I sure did!! :) Can you help me with my new problem? lol

12. Dec 12, 2011