Question

Indian H2 gas process PV square is equal to constant the ratio of work done by gas to change in internal energy is

• A. 2/3
• B. 0.4
• C. -0.4
• D. -2/3

Answer 1

The correct option is C -0.4

Given :Indian H2 gas process PV square is equal to constant the ratio of work done by gas to change in internal energy is

Solution :

$(PV{)}^2=constant=K$ eq-1

Work done = ${\int }_{V_1}^{V_2}P.dv$ eq-2

Internal energy U= $\frac{5}{2}nRT$ eq-3

$P=\frac{K}{V^2}$ eq-4

Substituting eq-4 in eq -2 we get

Work done = ${\int }_{V_1}^{V_2}\frac{K}{V^2}.dv$

On solving we get

Work done =$-K[\frac{1}{V_2}-\frac{1}{V_1}]$

W=$\frac{-K}{V_2}+\frac{K}{V_1}$ eq-5

Substituting eq-1 in eq -5 we get

W=$-P_2{V}_2+P_1{V}_1$

PV=nRT

W=$-(nR{T}_1-nR{T}_2)$ $\Rightarrow$ W=$-nR\Delta T$

Change in internal energy $\Delta U=\frac{5}{2}nR\Delta T$

Ratio =$\frac{W}{\Delta T}=-\frac{2}{5}$ = -0.4

The Correct Opt=C