The mass of one mole of a gas is $22.4 \times 10^{-3} \mathrm{~kg}$ and its specific heat ratio is 1.6. The…

The mass of one mole of a gas is $22.4 \times 10^{-3} \mathrm{~kg}$ and its specific heat ratio is 1.6. The speed of sound in the gas at STP is nearly
  1. 402
  2. 292
  3. 302
  4. 312

Solution

Mass of one mol gas, $\mathrm{m}=22.4 \times 10^{-3} \mathrm{~kg}$ Specific heat ratio, $\mathrm{r}=1.6$ Pressure at STP, $\mathrm{P}=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}^2$ Volume at STP, V $=22.4 \times 10^{-3} \mathrm{~L}$ Speed of sound is given as $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{P}}{\rho}}=\sqrt{\frac{\gamma \mathrm{PV}}{\mathrm{M}}}$ Substitute necessary values $\mathrm{v}=\sqrt{\frac{1.6 \times 1.01 \times 10^5 \times 22.4 \times 10^{-3}}{22.4 \times 10^{-3}}}$ $\mathrm{v}=4.02 \times 10^2 \mathrm{~m} / \mathrm{s}$

Asked in: AP EAMCET 2023 (18 May Shift 1)

Practice more Waves and Sound questions on Aicharya