# Homework Help: Thermodynamics and Internal Energy of a gas

1. Jan 22, 2014

### castrodisastro

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

2. Relevant equations
First law of thermodynamics: ΔEinternal=Q-W
W=∫VfVi P dV

3. 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
Einternal,final-Einternal,initial=Q-W
I can rearrange to solve for Einternal,final. Since no heat is lost in an adiabatic process, Q=0.

So now we have

Einternal,final = Einternal,initial - W
Einternal,final = 597 J - (-448275 J)
Einternal,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 Einternal,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 Einternal,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.

2. Jan 22, 2014

### 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)

3. Jan 22, 2014

### castrodisastro

Ah ok. I see. Pretty simple mistake. Thanks