Find the amount of work done to increase the temperature of one mole jof an ideal gas by `30^(@)C`, if it is expanding under condition `VooT^(2//3)`.

Options

A. `10 R`
B. `20 R`
C. `30 R`
D. `40 R`

Answer

B

Explanation

`W = int PdV = int (RT)/(V) dV`
Since `V = kT^(2//3)`
Hence, `(dV)/(V) = 2/3KT^(-1//3) dt :. (dV)/(V)=2/3 *(dT)/(T)`
Hence
`W = int_(T_1)^(T_2) 2/3 (RT)/(T) dT`
` = 2/3 R(T_(2)-T_(1)) = 2/3 R(30) = 20R`.