Question 1: Thermodynamics & KTG

Question

The velocity of sound in a gas is $1300 \mathrm{~m} / \mathrm{s}$ at STP and specific heat at constant pressure is $6.84 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$. The rms velocity at STP is $(R=1.98 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1})$

Accepted Answer

$v_{\mathrm{rms}}=v_{\mathrm{s}} \sqrt{\frac{3}{\gamma}}$
Also, $\gamma=\frac{C_p}{C_V}, R=C_p-C_V$
$\begin{aligned}
	ext{Given,} \quad & R=1.98 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \
& C_p=6.84 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} \
& C_p=4.86 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}, \gamma=1.41 \
& V_{	ext {rms }}=1300 \sqrt{2.13} \approx 1898 \mathrm{~m} / \mathrm{s}
\end{aligned}$

Answer

1300 m/s

Answer

2600 m/s

Answer

1898 m/s

Answer

650 m/s

Thermodynamics & KTG

The velocity of sound in a gas is 1300 \mathrm{~m} / \mathrm{s} at STP and specific heat at constant pressure is 6.84 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}. The rms velocity at STP is (R=1.98 \mathrm{~cal} \mathrm{~K}^{-1} \mathrm{~mol}^{-1})

Choose the correct answer: