# Work Done and final temperature of 5 mols of Ideal Gas

[SOLVED] Work Done and final temperature of 5 mols of Ideal Gas

## Homework Statement

Five moles of an ideal monatomic gas with an initial temperature of 129 degrees Celsius expand and, in the process, absorb an amount of heat equal to 1160 Joules and do an amount of work equal to 2020 Joules.

What is the final temperature of the gas?

## Homework Equations

$$W = -nR(T_f - T_i)$$

## The Attempt at a Solution

I have used the above formula before, and it worked then but doesn't appear to be working as well now

$$2020 - 1160 = -5*8.31(T_f - 129)$$

$$420 = -41.55(T_f - 129)$$

$$-10.1 = T_f - 129$$

$$T_f = -10.1 + 129$$

This gives me 118.9, which I have entered, and it says that:

" Not quite. Check through your calculations; you may have made a rounding error or used the wrong number of significant figures. "

I have tried also 120 as well, with the same response!

I doubt its the formula, because I have used it before? Any Ideas?

TFM

Doc Al
Mentor
How does the internal energy of an ideal monoatomic gas relate to its temperature? (Your formula is not quite right.)

Would that be this:

$$U = \frac{1}{2}nRT$$ per degree of Freedom.

?

TFM

Doc Al
Mentor
Yes! And how many degrees of freedom are there?

There are three degrees of Freedom, since it is a monatomic gas.

TFM

Doc Al
Mentor
Good. Now finish it up.

This would be:

$$U = \frac{3}{2}nRT$$

Can the T part be $$T = (Tf - Ti)$$

?

TFM

Doc Al
Mentor
This would be:

$$U = \frac{3}{2}nRT$$
Yes.

Can the T part be $$T = (Tf - Ti)$$
If you rewrite the above equation in terms of changes in U and T (as you should), yes.

Would the change in U still be 420?

TFM

I tried:

$$U = \frac{3}{2}nR(T_f - T_i)$$

and put in:

$$420 = \frac{3}{2}(5)(8.31)(T_f - 129)$$

IOt gave me an answer of 122, I put it in, And MP gas said itis wrong, and I have used up all my tries. Any ideas where I could have gone wrong?

TFM

Doc Al
Mentor
Arithmetic error: 1160 - 2020 = ?

Drat! I put 2020 - 1600 into my calculator by mistake!!! Putting in 860, I get the final temperature to be 115

Thanks for the help, even if my sillyness cost me ,

TFM