Work done to increase the temperature of one mole of an odeal gas by `30^@C`, if it is expanding under the condition `V prop T^(2//3)` is , `( R = 8.314 J// mol//K)`

Options

A. 116.2 J
B. 136.2 J
C. 166.2 J
D. 186.2 j

Answer

C

Explanation

` V prop T^(2//3) (Given) `
`V = K.T^(2//3)`
On differentiating the above equation
`dV = K*2/3*T`
` W = int PdV`
`implies W = int (RT)/(K*T^(2//3)) xx (K*2/3*T) [because PV = RT] ` `therefore W =( 2)/(3) RT = (2)/(3) xx 8.314 xx 30 = 166.2 J`