The mass of one mole of a gas is 22.4 times 1 | vedclass

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(A) The molar mass of the gas is $M = 22.4 	imes 10^{-3} \ kg/mol$.The specific heat ratio is $\gamma = 1.6$.At $STP$,the pressure is $P = 1.013 	im

Vedclass · Accepted Answer

$402$

Vedclass · Answer

(A) The molar mass of the gas is $M = 22.4 	imes 10^{-3} \ kg/mol$.The specific heat ratio is $\gamma = 1.6$.At $STP$,the pressure is $P = 1.013 	imes 10^5 \ Pa$ and the molar volume is $V_m = 22.4 	imes 10^{-3} \ m^3/mol$.The speed of sound in an ideal gas is given by the formula $v = \sqrt{\frac{\gamma P}{ho}}$.Since density $ho = \frac{M}{V_m}$,we can write $v = \sqrt{\frac{\gamma P V_m}{M}}$.Substituting the values: $v = \sqrt{\frac{1.6 	imes 1.013 	imes 10^5 	imes 22.4 	imes 10^{-3}}{22.4 	imes 10^{-3}}}$.$v = \sqrt{1.6 	imes 1.013 	imes 10^5} = \sqrt{1.6208 	imes 10^5} \approx \sqrt{162080} \approx 402.59 \ m/s$.Thus,the speed of sound is nearly $402 \ m/s$.

The mass of one mole of a gas is $22.4 \times 10^{-3} \ kg$ and its specific heat ratio is $1.6$. The speed of sound in the gas at $STP$ is nearly: (in $m/s$)

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