The Student Room Group

Perfect gas

The work done on the surroundings by a system when a gas expands reversibly from volume V1 to V2, while the external pressure p is adjusted so as to be constant, is given by

W(rev) = - integral of pdV between V1 and V2

calculate the work done for the expansion of n moles of a perfect gas at constant temperature, i.e under isothermal conditions

I have no idea how to do this, any help please?
Reply 1
pV=nRTpV=nRT

Rearrange to make p the subject, then

W=V1V2nRTVdV=nRTV1V21VdVW=-\int_{V_{1}}^{V_{2}}\frac{nRT}{V}dV=-nRT\int_{V_1}^{V_2}\frac{1}{V}dV

Then
integrate wrt V, (it's the natural logarithm).

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