The speed of sound in an ideal gas is given by the relationship v = R T M , wher

Question

The speed of sound in an ideal gas is given by the relationship v=RTM, where R - the universal gas constant = 8.314 J/molK; T - the absolute temperature; M - the molar mass of the gas in kg/mol; and is a characteristic of the specific gas. For air, = 1.4.

Part A

Calculate how much faster sound travels in summer than in winter. Assume that air is 20% oxygen and 80% nitrogen. For summer, assume a temperature Tsummer = 303 K and a winter temperature Twinter = 283 K.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

v_sound = sqrt(gamma*R*T/M)

M is the molar mass of the air = 29*10^-3 kg/mol

R is the universal gas constant = 8.314 J/mol K

T = 303 K

gamma = 1.4

vsummer = sqrt(1.4*8.314*303/(29*10^-3)) = 348.73 m/sec

vwinter = sqrt(1.4*8.314*283/(29*10^-3)) = 337.02 m/sec

required value is

vsummer - vwinter = 348.73-337.02 = 11.71 m/sec

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