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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 Cp and Cv of the gas.

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
6 years ago
Sol. f = 5 * 10^3 Hz, T = 300 Hz, λ/2 = 3.3 cm ⇒ λ = 6.6 * 10^-2 m V = fλ = 5 * 10^3 * 6.6 * 10^-2 = (66 * 5) m/s V = fP/f [Pv = nRT ⇒ P = m/mV * Rt ⇒ PM = foRT ⇒ P/fo = RT/m] = √γRT/m(66 * 5) = √γ * 8.3 * 300/32 * 10^-3 ⇒ (66 * 5)^2 = γ * 8.3 * 300/32 * 10^-3 ⇒ γ = (66 * 5)^2 * 32 * 10^-3/8.3 * 300 = 1.3995 C base v= R/γ – 1 = 8.3/0.3995 = 20.7 J/mol-k, C base P = C base V + R = 20.77 + 8.3 = 29.07 J/mol-k.
Navjyot Kalra
askIITians Faculty 654 Points
6 years ago
Sol f = 5 * 10^3 Hz, T = 300 Hz, λ/2 = 3.3 cm ⇒ λ = 6.6 * 10^-2 m V = fλ = 5 * 10^3 * 6.6 * 10^-2 = (66 * 5) m/s V = fP/f [Pv = nRT ⇒ P = m/mV * Rt ⇒ PM = foRT ⇒ P/fo = RT/m] = √γRT/m(66 * 5) = √γ * 8.3 * 300/32 * 10^-3 ⇒ (66 * 5)^2 = γ * 8.3 * 300/32 * 10^-3 ⇒ γ = (66 * 5)^2 * 32 * 10^-3/8.3 * 300 = 1.3995 C base v= R/γ – 1 = 8.3/0.3995 = 20.7 J/mol-k, C base P = C base V + R = 20.77 + 8.3 = 29.07 J/mol-k.

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