# Homework Help: Compressing ideal gas isothermally, calc work

1. Apr 15, 2010

### gcooke

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

10 moles of an ideal gas are compressed isothermally and reversibly from 1 to 10 atmospheres at 300K. Determine the work done ON the gas.

2. Relevant equations

dw=-PdV
PV=nRT

3. The attempt at a solution

dT=0
T=300K
dP=10atm

calc dV from ideal gas law = 2.27e10 m^3

so now we have dV for work eqn, but P is not constant?

Thanks.

Last edited: Apr 15, 2010
2. Apr 15, 2010

### irycio

As much as I don't like thermodynamics, it doesn't seem very complicated.
p1V1=nRT
which allows you to calculate the first volume.
Equation nr.2:
p2V2=nRT
allows you to calculate 2nd volume. Hence you've got your integrating limits.
Now, I wish I knew how to use TeX in here :/.
Anyway,
$$W=\int\limits_{v_1}^{v_2} pdV$$
As you mentioned, p is not constant, but you can, again, calculate it easily from clapeyron's equation:
pV=nRT. And then substitute p under integral with what you've got, integrate. Should get natural logarithm.

Last edited: Apr 15, 2010
3. Apr 15, 2010

### gcooke

Thank you, irycio!