- #1

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## Main Question or Discussion Point

I was able to derive the work done in a reversible isothermal expansion. There as the P changes to P-dP, the volume increases by dV and hence the internal pressure also decreases by dP and equilibrium is maintained. (Thanks to @Nugatory and @Chestermiller fo r explaining it).

Now when we take an irreversible isothermal expansion in the book the ##P_{ext}## is taken constant and then dV is integrated to get

$$W = -P_{ext}(V_2-V_1) $$

But for reversible isothermal expansion, the ##P_ext## is taken as a variable. That is it is taken as ##\frac{nRT}{V}## and then integrated to get

$$W = RTln(\frac{V_2}{V_1})$$

why is ##P_{ext}## different for the two cases?

Now when we take an irreversible isothermal expansion in the book the ##P_{ext}## is taken constant and then dV is integrated to get

$$W = -P_{ext}(V_2-V_1) $$

But for reversible isothermal expansion, the ##P_ext## is taken as a variable. That is it is taken as ##\frac{nRT}{V}## and then integrated to get

$$W = RTln(\frac{V_2}{V_1})$$

why is ##P_{ext}## different for the two cases?