Calculating Internal Energy Change in a Gas Under Constant Pressure

[duds1234]

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

Homework Statement

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)?

Homework Equations

a) $W=-PΔV$
b) $ΔU=Q+W$

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!

 

[DeltaFunction]

If your answer to part a is correct, then I can't see what's wrong with your answer to part b (see EDIT)

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

 

[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.

 

[DeltaFunction]

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

 

[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.

 

[DeltaFunction]

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