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Question

A sealed container of an ideal gas at 320 K, 0.77 m^3, and 140000 Pa is compressed isothermally to 0.26m^3. What is the work done on the gas during this process?

Answer 1

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The work done BY the gas would be

W = integral from v1 to v2 of p dv, but p = nRT/v = (p1 v1)/v.

So you want the integral of (p1 v1) dv/v, which comes out to

(p1 v1)*ln(v2/v1) = (140000 Pa)(0.77 m^3)*ln(0.26/0.77)

= -117 kJ.

Then the work done ON the gas is 117 kJ.