- 50

- 2

**1. Homework Statement**

Two moles of a monatomic ideal gas are at a temperature of 300K. The gas expands reversibly and isothermally to twice its original volume. Calculate the work done by the gas, the heat supplied and the change in internal energy.

So:

T = 300K; ΔT = 0

n = 2; R = 8.314 J K

^{-1}mol

^{-1}

V

_{2}= 2V

_{1}

Reversible process ⇒ work is path independent.

**2. Homework Equations**

PV = nRT

W = -PdV

U = W + Q

**3. The Attempt at a Solution**

PV = nRT ⇒ P = nRT / V

dW = -PdV ⇒ W = - ∫ PdV = - nRT ∫ [dV / V] = nRT [ln |V

_{2}- V

_{1}|] = nRT ln V

_{1}

This isn't very helpful as I have no actual figure for what V

_{1}is.

I've tried to come up with something based on how the work is path independent (so W = P

_{2}V

_{2}- P

_{1}V

_{1}= V

_{1}[P

_{2}- P

_{1}]) but I've just confused myself, as ΔT = 0 means that P

_{1}V

_{1}= P

_{2}V

_{2}= nRT, so that would mean that W = 0 which isn't right. I must be going wrong with my assumptions somewhere - any pointers would be much appreciated!

Edit: I'm confident that once I get past the first stumbling block & calculate the work done I can fire ahead & calculate Q and ΔU. Thanks in advance!