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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?
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