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)`.

Answer

`166.2`

Explanation

`V prop T^(2//3) rArr P prop V^(1//2) rArr PV^(-1//2) = "constant"`
Comparing it with `PV^n` = constant we get
`n = -1 //2`
`C = C_V - R/(n-1)` or ` C = C_V + (2R)/3`
Now, `Delta Q = n C Delta T =n C_v Delta T + n((2R)/3) Delta T`
But from first law: `Delta Q = Delta U + W ` and ` Delta U = n C_V Delta T` ( for any process )
`rArr" "Delta Q = Delta U + n((2R)/3)Delta T " "rArr" "W = n ((2R)/3)Delta T = 166J`