Question

What is the equation for work done in a reversible isothermal process (processes 1 to 3 in this case)? My course tutor wrote down (P3V3)ln(V1/V3), what is this?

Answer 1

The expression of work for that process
A=-nRT*ln(V₃/V₁)
where V₁-the initial volume, V₃ -the final volume.
From the equation of state, if our substance is a gas we can get an approximate value of the expansion work using the ideal gas equation of state
pV=nRT
Since T=const, we can say that nRT=p₃V₃
also from the properties of ln-function
ln(V₃/V₁)=-ln(V₁/V₃)
So we have
A=p₃V₃*ln(V₁/V₃) that's exactly what ur teacher wrote.