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Grade: 11
        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.
5 years ago

Answers : (2)

Kevin Nash
askIITians Faculty
332 Points
							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.

						
5 years ago
Navjyot Kalra
askIITians Faculty
654 Points
							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.

						
5 years ago
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