Calculate the speed of sound in oxygen from the following data:
Mass of 22.4 litre of oxygen at STP = 32g, $C_{V} = 2.5 R$

540 m/s

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420 m/s

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315 m/s

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250 m/s

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Solution

The correct option is C 315 m/s
$C_{P} - C_{V} = R C_{P} = R + C_{V} = R + 2.5 R = 3.5 R γ = \frac{C_{P}}{C_{V}} = \frac{3.5 R}{2.5 R} = 1.4$
Density of oxygen at STP $= \frac{m a s s}{v o l u m e}$
$= \frac{32 \times 10^{- 3} k g}{22.4 \times 10^{- 3} m^{3}}$
$ρ = 1.4286 k g m^{- 3}$
Normal pressure or standard pressure = $1.013 \times 10^{5} P a$
$V = \sqrt{\frac{γ P}{ρ}} = \sqrt{\frac{1.4 \times 1.013 \times 10^{5}}{1.4286}} V = 315 m s^{- 1}$

Ans: $315 m s^{- 1}$

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