Find the amount of work done to increase the temperature of one mole of ideal gas by `30^(@)C` .if its is expanding under the condition `V prop R^(2//3) (R = 8.31 J//mol -K):`

Options

A. `16.62J`
B. `166.2J`
C. `1662J`
D. `1.662J`

Explanation

`PV=mRT" " T`
Process `VpropT^(2//3)` or `TpropV^(3//2)`
For `PV^(x)=" constant" PVpropV^(3//2)`
`PV^(-1//2)` constant
`W=(nR)/(x-1)(dt)`
`=(1R)/(-1-(1)/(2))(-30)=(60R)/(3)=20R=166.2`