Question

Find the amount of work done to increase the temperature of one mole of an ideal gas by 30⁰C if it is expanding under the condition V µ T^2/3 –

• A. 166.2 J
• B. 136.2 J
• C. 126.2 J
• D. None of these

Answer 1

Answer: (A)

166.2 J

Answer 2

PV = RT for 1 mole

W = $\int_{}^{}{PdV}$ = $\int_{}^{}\frac{RT}{V}$dV

V = CT^2/3

\ dV = $\frac{2}{3}$ CT^–1/3 dT or $\frac{dV}{V}$ = $\frac { 2 } { 3 }$ $\frac{dT}{T}$

\ W = $\int_{T_{1}}^{T_{2}}{RT\left\lbrack \frac{2}{3} \right\rbrack\frac{dT}{T} = \frac{2}{3}}$R(T₂ – T₁) = 166.2