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Three moles of an ideal gas are compressed from 5.5*10^-2 to 2.5*10^-2 m^3. During the compression, 6.1*10^3J of work is done on the gas, and heat is removed to keep the temperature of the gas constant at all times. Find the temperature of the gas.

I posted this question few hours ago, and someone gave me such hints to do it. However, I don't quite get it, can anyone please explain more about it?THANKS A LOT!

p V = n R T is state equation before and after
Now work done at constant temp

dW = -p dV
but p = (n R T)/V and here n R T is constant given
so
dW = -(nRT) dV/V
so
work done = (nRT) ln(V1/V2)

by the way, that is also the heat out since internal energy depends only on T which is constant.

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sTELLA

  1. Stella,
    I assumed that you have had calculus.
    If you have not, then your book must say something like:

    For an ideal gas:
    With compression at constant temperature,
    work in = (n R T) ln (V1/V2)
    or
    With compression at constant temperature
    heat out = (n R T) ln (V1/V2)

    Since change in internal energy = heat in - work out
    and internal energy depends only on temperature
    your work in is the same as the heat out
    You are given the work in, so you have :

    work in
    n, number of moles
    R gas constant
    V1 and V2
    so you can calculate T

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    Damon

  2. work in = (n R T) ln (V1/V2)

    what is the "1n" standing for?

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    sTELLA

  4. ln is natural log. Log to the base e. It is on your calculator, probably on the same key as e^x

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    Damon

  5. This must be in your physics book. Look in the index for isothermal compression or expansion or simply compression or expansion. It may be in a paragraph on "work done during volume changes".

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