Derive an expression for maximum work in isothermal reversible expansion of two mole of an ideal gas.

Explanation

an expresion for maximum work in isothermal reversible expansion of two mole of ideal gas : We can also relate work to internal pressure of the system under reversible condition if volume change from `V_(1)` to `V_(2)`
`W_("rev")=-int_(V_(1))^(V_(2)) P_("in") dv` we know
`W_("rev")=-int_(V_(1))^(V_(2)) P_(ex) dv=-int_(V_(1))^(V_(2)) (P_("in") pm d_(p)) dV`
`=-int_(V_(1))^(V_(2))(P_("in") dV pm dp. dV)`
dp and dV are infinite small so that dp.dV is neglected.
`W_("rev")=-int_(V_(1))^(V_(2)) P_("in") dV`
Now pressure of gas `P_("in")=P` can be expressed in terms of its volume through gas equation
`PV=nRT`
`P=n/V RT`
Therefore, at constant temperature (for isothermal process)
`W_("rev")=-int_(V_(1))^(V_(2)) nRT (dV)/V`
`=-nRT ln (V_(2))/(V_(1))`
`W_("rev")=-2.303 nRT "log" V_(2)/V_(1)`
for `n=2`
`W_("rev")=-4.606 RT "log" V_(2)/V_(1)`