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 heaitng of gas
`W_(a) =- PDeltaV =- P(V_(2)-V_(1))`
`=- P ((nRT_(1))/(P)-(nRT_(1))/(P))`
`=- nR (T_(2)-T_(1))`
`=- 1 xx 8.314(373 - 273)`
`=- 831.14J`
b. Now the work equivalent to `831.4` cal is used up in causing reversible isothermal expansion of gas at `0^(@)C`, then
`W_(R) =- 2.303nRT log_(10). (P_(1))/(P_(2))`
`-831.4 =- 2.303 xx 1 xx 8.314 xx 273 log_(10). (P_(1))/(P_(2))`
`:. P_(t) = 0.694atm`