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.

Estimate the speed of sound in air at standard temperature and pressur

1.	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.
Answer» Solution :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.