Thermodynamics and Internal Energy of a gas

[castrodisastro]

Homework Statement

The internal energy of a gas is 597 joules. The gas is compressed adiabatically and its volume decreases by 129 cm³. If the pressure applied on the gas during compression is 3.43 atm, what is the internal energy of the gas after adiabatic compression?

Homework Equations

First law of thermodynamics: ΔEinternal=Q-W
W=∫VfVi P dV

The Attempt at a Solution

I first converted 3.43 atm to Pascals. This gave me 3.475*10⁵ Pascals.
I converted 129 cm³ to meters. This gave me 1.29 meters.

Since I need to use the first law of thermodynamics. I will need to know the work done to the system. I calculated this by taking the integral of 3.475*10⁵ from 0m³ to 1.29m³ (since we were only given the change in volume I used 0m³ as my initial volume). My answer was 448275 Pa*m³ = 448275 Joules.

Rewriting the first law of thermodynamics as
E_{internal,final}-E_{internal,initial}=Q-W
I can rearrange to solve for E_{internal,final}. Since no heat is lost in an adiabatic process, Q=0.

So now we have

E_{internal,final} = E_{internal,initial} - W
E_{internal,final} = 597 J - (-448275 J)
E_{internal,final} = 448872 J

The reason I am confused is because the magnitude of the internal energy seems way too high. my answer could be correct but the reason I am suspiscious is because when I look at example problems done by other people, they convert atm to Pascals the same way I did, and when they calculate the work, the amount is of the same magnitude as I calculated (10⁵), but when they add that work to their E_{internal,initial}, their amount of work in joules magically reduces to a value of magnitude 10³. I say magically because they provide no explanation for this decrease. At first I thought maybe the conversion was from atm to kPa but the textbook, and online sources, state 1.0 atm to be equal to 101,325 Pascals. So is my answer correct or am I forgetting a step before I subtract the work from the E_{internal,initial}? I made sure to account for all units and my answer came out to Joules as they should but I am just concerned that I may not be decreasing the order of magnitude if I am supposed to. Thanks in advance.

 

[lightgrav]

1 cubic meter is 1000 liters, which is 1 million cubic centimeters. You ought to be adding about 44.8 J work.
(adiabatic process is NOT constant pressure; they probably gave the final pressure)

 

[castrodisastro]

Ah ok. I see. Pretty simple mistake. Thanks