The densities of nitrogen and oxygen at NTP are $1.25 k g / m^{3}$ and $1.43 k g / m^{3}$ respectively .If the speed of sound in oxygen at NTP is 320 m/s. calculate the speed in nitrogen, under the same conditions of temperature and pressure. (y for both the gases is 1.4)

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Solution

Density of Nitrogen at $N T P = 1.25 k g / m^{3}$
Density of Oxygen at $N T P = 1.43 k g / m^{3}$
Speed of sound in oxygen is $320 m / s$
Speed of sound in gases $= \sqrt{\frac{y R T}{M}}$
$y = 1.4$ given for both gases
$320 = \frac{\sqrt{1.4 \times 8.314 k j / k m o l e k \times 293}}{M O_{2}}$
$(320)^{2} = \frac{1.4 \times 8.314 K J / k m o l e k \times 293}{M O_{2}}$
$M_{O_{2}} = \frac{1.4 \times 8.314 k J / k m o l e k \times 293}{320 \times 320}$
$M_{O_{2}} = 33.30 k g / k m o l e$
Density $= \frac{M a s s}{v o l u m e}$
$1.43 = \frac{33.30}{V}$
$V = 23.25$
For Nitrogen $(N_{2})$
$1.25 = \frac{M N_{2}}{23.28}$
$M N_{2} = 29.1 k g / k m o l e$
Speed of sound in $N_{2} = \sqrt{\frac{1.4 \times 8.314 \times 293}{\frac{29.1}{1000}}}$
Speed of sound in $N_{2} = 342.33 m / s$

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The densities of nitrogen and oxygen at NTP are 1.25 kg/m3 and 1.43 kg/m3 respectively .If the speed of sound in oxygen at NTP is 320 m/s. calculate the speed in nitrogen, under the same conditions of temperature and pressure. (y for both the gases is 1.4)

The densities of nitrogen and oxygen at NTP are $1.25 k g / m^{3}$ and $1.43 k g / m^{3}$ respectively .If the speed of sound in oxygen at NTP is 320 m/s. calculate the speed in nitrogen, under the same conditions of temperature and pressure. (y for both the gases is 1.4)