Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive modes is 3.3 cm. Calculate the specific heat capacities $C_{p}$ and $C_{v}$ of the gas

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Solution

F = $5 \times 10^{3} H z,$

$T = 300 K, \frac{1}{2} = 3.3 c m$

$∴ l = 6.6 \times 10^{- 2} m$

$V = f t = 5 \times 10^{3} \times 6.6 \times 10^{- 2}$

= $(66 \times 5) = 330 m / s$

v = $\sqrt{\frac{γ R T}{M}} o r V^{2} = \frac{γ R T}{M}$

$∴ γ = \frac{330 \times 330 \times 32}{8.3 \times 300 \times 100} = 1.3995$

$C_{v} = \frac{R}{γ - 1} = \frac{8.3}{0.3995}$

= 20.7 J mol-K

$C_{p} = C_{v} + R$

= 20.7 J + 8.3

= 29.07 J/mol-K

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