Question

$1\text{g}$ mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. Find the change in internal energy $(\gamma =1.4)$.

• A. $1169.5\text{J}$
• B. $769.5\text{J}$
• C. $-1369.5\text{J}$
• D. $-969.5\text{J}$

Answer 1

The correct option is C $-1369.5\text{J}$

Use $T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
Given:$V_2=2V_1$
or $T_2=\frac{T_1{V}_1^{\gamma -1}}{V_2^{\gamma -1}}=\frac{273}{(2{)}^{0.4}}=207\text{K}$
Change in internal energy
$\Delta U=C_v\Delta T=\frac{R}{(\gamma -1)}(T_2-T_1)$
$=\frac{-8.31(273-207)}{1.4-1}=-1369.5\text{J}$