the speed of sound at 0 degrees celsius is 332 m/s. At what temperature will it be 664 m/s.
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Speed of sound v in an ideal gas : is proportional to the square root of absolute temperature T.
v₂ / v₁ = √(T₂ / T₁)
664 / 332 = √ (T₂ / 273.15)
T₂ = 4 * 273.15 °K = 1092.6°K
T₂ = 1092.6°K - 273.15 = 819.45 °C
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[tex]v=\sqrt{\frac{\gamma\ R\ T}{M}}=\sqrt{\frac{\gamma\ P}{\rho}}=\sqrt{\frac{\gamma\ k_B\ T}{m}}[/tex]
γ = ratio of specific heats
T = absolute temperature
R universal gas constant.
M = molar mass of the gas.
k_B = Boltzmann's constant
m = mass of a molecule of gas.
v₂ / v₁ = √(T₂ / T₁)
664 / 332 = √ (T₂ / 273.15)
T₂ = 4 * 273.15 °K = 1092.6°K
T₂ = 1092.6°K - 273.15 = 819.45 °C
===========================
[tex]v=\sqrt{\frac{\gamma\ R\ T}{M}}=\sqrt{\frac{\gamma\ P}{\rho}}=\sqrt{\frac{\gamma\ k_B\ T}{m}}[/tex]
γ = ratio of specific heats
T = absolute temperature
R universal gas constant.
M = molar mass of the gas.
k_B = Boltzmann's constant
m = mass of a molecule of gas.
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