Change in Internal Energy

1. Aug 31, 2013

duds1234

Hello, this is my first post, so I apologize in advance if it's not quite up to par.

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

A gas is compressed at a constant pressure of 0.639 atm from 5.41 L to 2.3 L. In the process, 470 J of energy leaves the gas by heat.
a) What is the work done on the gas (J)?
b) What is the change in its internal energy(J)?

2. Relevant equations

a) $W=-PΔV$
b) $ΔU=Q+W$

3. The attempt at a solution

a)
$P = 0.639atm {\frac{1Pa}{9.872*10^-6atm}} = 64728.52512Pa$
$ΔV = V_f - V_i = 2.3L - 5.41L = -3.11L {\frac{1*10^{-3}m^3}{1L}} = -0.00311m^3$
$W = -P ΔV = -6.4728.52512Pa * -0.00311m^3 = 201.3057131J$

I submitted my answer to part a and it was correct. Part b is what I need help with. I believe that I am doing it correctly, but my answer is returned as incorrect. My incorrect work and answer appears below.

b)
$ΔU = Q + W = -407J + 201.3057131J = -205.6942869J$

Any insight into why my work/answer for part b is incorrect would be greatly appreciated!

2. Aug 31, 2013

DeltaFunction

Is this a multi choice question that is automatically assessed?

EDIT: Just noticed that in the question statement you say that 470J of energy leaves, but in the calculation for part b you use the figure 407J

Last edited: Aug 31, 2013
3. Aug 31, 2013

duds1234

Unfortunately, this isn't a multiple choice question. I have to submit my answers electronically and a computer grades them. I have confirmation that part a is correct and that my answer for b is incorrect.

4. Aug 31, 2013

DeltaFunction

Ok. Can you confirm which value of heat leaving the gas is correct: 407 J or 470 J

5. Aug 31, 2013

duds1234

It is 470, thus this would be my error in part b. Thank you very much for helping me find my silly mistake. The correct answer would be -268.6942869J.

6. Aug 31, 2013

DeltaFunction

You're welcome. It happens to everyone now and then!