Question

The specific heats of an ideal gas at constant pressure and constant volume are $525 \, J$ $kg^\circ C^{- 1}$ and $315 \, J \, kg^\circ \, C^{- 1}$ respectively. Its density at NTP is

• A. $0.64 \, kg \, m^{- 3}$
• B. $1.20 \, kg \, m^{- 3}$
• C. $1.75 \, kg \, m^{- 3}$
• D. $2.62 \, kg \, m^{- 3}$

Answer 1

Answer: (C)

If $M$ is molecular mass of the gas, then from
$M\left(C_{p} - C_{v}\right)=R$
$M=\frac{8.31}{210}=0.0392$
If $\rho $ is density of the gas at NTP, then mass of 1 $m^{3}$ of gas at NTP $=\rho $ kg
$\therefore$ Mass of $22.4 L \left(=22.4 \times 10^{-3} m ^{3}\right)$ of gas at NTP $=\rho \times 22.4 \times 10^{-3} kg$, which is the molecular mass of the gas
$\therefore \, \rho \times 22.4\times 10^{- 3}=0.0392$
$\rho =\frac{0.0392}{22.4 \times 10^{- 3}}=1.75 \, kg \, m^{- 3}$