Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities C_p and C_vof the gas.

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Solution

Frequency of standing waves, f = 5 × 10³ Hz
Temperature of oxygen, T = 300 K
From Kundt's tube theory, we know that
$\frac{l}{2}$ = node separation = 3.3 cm
∴ l = 6.6 × 10⁻² m
Also,
v = fl = 5 × 10³ × 6.6 × 10⁻²
= (66 × 5) = 330 m/s
$v = \sqrt{\frac{γ R T}{M}} v^{2} = \frac{γ R T}{M} ∴ γ = \frac{330 \times 330 \times 32}{8.3 \times 300 \times 100} = 1.3995 S pecific heat at constant volume, C_{v} = \frac{R}{γ - 1} = \frac{8.3}{0.3995}$

= 20.7 J mol-K

Specific heat at constant pressure, C_p = C_v + R
C_p= 20.7 + 8.3
C_p= 29.0 J/mol-K

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Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities Cp and Cv of the gas.

Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities C_p and C_vof the gas.