Question

One mole of monatomic gas and three moles of diatomic gas are put together in a container. The molar specific heat (in $JK ^{-1} mol ^{-1}$ ) at constant volume is (Let $R=8 \,JK ^{-1} mol ^{-1}$ )

• A. 18
• B. 19
• C. 20
• D. 21

Answer 1

Answer: (A)

$n_{1}=1 $ mole $ f_{1}=3$
$n_{2}=3 $ moles $ f_{2}=5 $
$R=8 \,JK ^{-1} mol ^{-1} $
Molar specific heat are given by the weighted means of the gases.
$C_{v_{f}}=\frac{n_{1} \times C_{v_{1}}+n_{2} \times C_{V_{2}}}{n_{1}+n_{2}} $
$C_{v_{f}}=\frac{1 \times \frac{3}{2} R+3 \times \frac{5}{2} R}{4} $
$=\frac{3}{8} R+\frac{15}{8} R$
$=\frac{18}{8} R $
$C_{v_{f}}=18$