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Estimate the speed of sound in air at st...

Estimate the speed of sound in air at standard temperature and pressure. The mass of 1 mole of air is `29.0 xx 10 ^(-3)kg.`

Text Solution

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We know that at STP, volume of one mole of gas is `V= 22.4 ` litre `=22.4 xx 10 ^(-3) m ^(3)`
and pressure is `P =1 ` atm `= 1.01 xx 10 ^(5) (N)/(m^(2))`
Density of air at STP,
` rho (M)/(V) = (29 xx 10 ^(-3))/(22.4 xx 10 ^(-3)) = 1.29 (kg)/(m^(3))`
Approximate value of speed of sound in air at STP can be found out using following Newton.s formula,
`v = sqrt ((P)/(rho)) = sqrt ((1.01 xx 10- ^(5))/(1.29)) =279.8ms ^(-1) =280 ms ^(-1)`
Practicaly, speed of sound in air at STP is found to be `331 ms ^(-1).` Hence, percentage error in above approximation would be,
`(331-280)/(331) xx100% =15.41%`
Thus, here Newton.s formula gives speed of sound in air at STP, `15.41%` less than the experimental value.
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