What work is to be done on `2mol` of a perfect gas at `27^(@)C` it is compressed reversibly and isothermally from a pressure of `1.01 xx 10^(5) Nm^(-2) to 5.05 xx 10^(6)Nm^(-2)`?

Options

A. work done on the gas is `1.9518 xx 10^(4)J`
B. Free energy change for the process is `-1.9518 xx 10^(4)J`
C. work done on the gas is `1.19 xx 10^(7)J`
D. Free energy change for the process is `-1.19 xx 10^(7)J`

Answer

A, B

Explanation

reversible process: `W_(rev) = -2.303 nRT log_(10).(p_(1))/(p_(2))`
`= -2.303 xx 2 xx 8.314 xx 300 log_(10).(1.01 xx 10^(5))/(5.05 xx 10^(5))`
`+ 1.9518 xx 10^(4) "joule"`
Since W reversible is a measure of free change
`-Delta G = -W_(rev) = -W_(max) = 1.9518 xx 10^(4)J`