One mole of an ideal gas is heated at constant pressure from `0^(@)C` to `100^(@)C`.
a. Calculate the work done.
b. If the gas were expanded isothermally and reversibly at `0^(@)C` from `1 atm` to some othe pressure `P`, what must be the final pressure if the maixmum work is equal to the work in `(a)`?

Explanation

(a) Work involved in heating of gas
`W_(a)=-PDeltaV=-P(V_(2)-V_(1))`
`=-P((nRT_(2))/P-(nRT_(1))/P)`
`=-nR(T_(2)-T_(1))=-1xx1.987(373-273)`
`=-198.7 cal`
(b) Now the work equivalent to `198.7 cal` is used up in causing reversible isothermal expansion of gas at `0^(@)C`, then
`W_(R)=-2.303 nRT "log"_(10)(P_(1))/(P_(2))`
`:. -198.7=-2.303xx1xx1xx1.987xx273"log"_(10)(1)/(P_(t))`
`:. P_(t)=0.694 atm`