# Homework Help: Stuck with a gas expansion problem?

1. Oct 23, 2008

### jeebs

Hi, i think i've got the first part of this question done but im stuck with the rest, so i'll post the lot in case you think i have the first part wrong.

a) Derive and expression for the work done by an ideal gas when it expands isothermally at temperature T from a volume V1 to V2.

b) calculate the work done when T = 25 degrees C and V2 = 3V1.

c) calculate the magnitude and direction of the flow of heat during the above process.
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Here is my attempt. for the first part, i am imagining a gas expanding like burning petrol in a car engine, the gas is forcing the piston of area A a distance x along the cylinder:

a) work done dW = F.dx (work = force x displacement).

F = pA (force = pressure x area). change in volume dV = A.dx

therefore dW = pA.dx = p.dV, so W = ∫ p.dV

and since pV = nRT we can write that W = nRT∫(1/V).dV = (nRT).ln(V)

so, W = (nRT).ln(V2) - (nRT).ln(V1) = nRT.ln(V2/V1).

b) to calculate the work done, i plugged the numbers into the equation (the ln(V2/V1) part becomes ln(3) ) but i do not know the number of moles, therefore i am stuck with the n term.

the closest i can get to an answer is 2720.58 Joules per mole.

can anyone help me out here?

EDIT: apologies, it turns out that my problem sheet had information missing from it. there was one mole of gas present, n=1.
so part b) is completed.

c) i have no idea how to do this.

does anyone know what i have to do? i am very grateful for any help.

thanks.

Last edited: Oct 23, 2008
2. Oct 23, 2008

### nasu

Use the first law of thermodynamics.
Hint: Isothermal process, ideal gas. what is the change in internal energy?