Fixed mass of an ideal gas collected in a 24.64 litre sealed rigid vessel at 10 atm is heated from `-73^(@)C` to `27^(@)C` calculate change in gibbs free energy if entropy of gas is a function of temperature as `S=2+10^(-2)T(J//K)(1l atm=0.1kJ)`

Options

A. `123.5J`
B. `1281.5J`
C. `781.5J`
D. 0

Answer

C

Explanation

At constant volume `(p_(1))/(T_(1)) = (p_(2))/(T_(2)) rArr p_(2) = p_(1) (T_(2))/(T_(1)) = (3)/(2)`
`rArr dG = V dp - S dT`
`= V deltap- underset(200k)overset(300k)int 2 + 10^(-T) T dT`