1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Stuck with a gas expansion problem?

  1. Oct 23, 2008 #1
    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.
    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.

    Last edited: Oct 23, 2008
  2. jcsd
  3. Oct 23, 2008 #2
    Use the first law of thermodynamics.
    Hint: Isothermal process, ideal gas. what is the change in internal energy?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook