# Thermal Physics Adiabatic Heating Problem

1. Jan 8, 2014

### Borntofly123

Greetings all,

My first post here on this forum. I'm currently revising for exams and have got stuck on a question where I'm not sure where I'm going wrong...

Question:
1g of iron filings at 500 °C are inserted into a sealed 20 litre vessel containing 1 mol of an ideal monatomic gas at a pressure of 10^5 Pa.

1. Assuming the walls of the vessel are of negligible heat capacity and the process is adiabatic, what is the final temperature of the system?
(specific heat capacity of iron = 0.45 kJ kg–1K–1.)

The attempt at a solution:
I start by arguing that as this is a sealed environment, then the energy lost by the iron equals the energy gained by the gas.

Therefore for the iron Q=mc*deltaT where deltaT=T(final) - (500+273K)

As this is adiabatic, then the potential gained by the gas is given by dU=C(v)dT where C(v) is the heat capacity of constant volume for the gas given by nRf/2 where f is the number of degrees of freedom, in this case 3 for a monatomic gas.

Then equating mc(T(final)-773)=1.5R(T(final)-(pV/nR)) where pV/nR is used to find the initial temperature of the gas, leads to T(final) found to be 221K, which is clearly wrong. I'm told the answer is 260K.

Any pointers or corrections would be greatly appreciated.

2. Jan 8, 2014

### Staff: Mentor

It looks like you are missing a minus sign in your equation. The change in the combined internal energy of the filings and the gas should be zero. Otherwise, everything else looks OK.

Chet

3. Jan 9, 2014

### Borntofly123

So simple, yet so frustrating. Thank you for your help, much appreciated!

4. Jan 9, 2014

### Staff: Mentor

I hope you're not too frustrated. You got the hard part completely right. You just made a minor error at the end.