Question

Find the amount of work done to increase the temperature of one mole of an ideal gas by `30^(@)C`, if it is expanding under condition `VooT^(2//3)`.
A. `32R`
B. `15R`
C. `20R`
D. `25R`

Answer 1

Correct Answer - C
Idea gas equation `PV = nRT`
for one mole of ideal gas `PV = RT implies P = (RT)/(V)`
Given that `V prop T^(2//3) or V = kT^(2//3)`..(i)
Differentiating equation (i)
`dV= k2/3 T^(-1//3)dT` ..(ii)
Work done `dW = PdV = ((RT)/(V)) *k 2/3 T^(-1//3) dT`
`dW = (RT)/(kT^(2//3)) * k * 2/3 T^(-1//3) dT = 2/3 RdT` ..(iii)
Integrating equation (iii)
`W = int dW = 2/3 int_(T_1)^(T_2) dT = 2/3 R(T_2-T_1) = 2/3 RDelta T`
Total work done, `W = 2/3 xx R xx 30 = 20 R`.