Question

$1g$ 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. $\mathrm{11.695.5}J$
• B. $769.5J$
• C. $1369.5J$
• D. $969.5J$

Answer 1

Answer: (C)

$1369.5J$

As it is an adiabatic process we use
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
or $T_2=\frac{T_1{V}_1^{\gamma -1}}{V_2^{\gamma -1}}=\frac{273}{(2{)}^{0.4}}=207K$
Change the Internal Energy $\Delta U=\frac{R}{(\gamma -1)}(T_1-T_2)$
$=\frac{8.31(273-207)}{1.4-1}=1369.5J$