A long tube contains air at a pressure of `1 atm` and a temperature of `107^(@) C`. The tube is open at one end and closed at the other by a movable piston. A tuning fork near the open end is vibrating with a frequency of `500 Hz`. Resonance is produced when the piston is at distance `19 , 58.5 and 98 cm` from the open end.
The molar mass of air is `28.8 g//mol`. The ratio of molar heat capacities at constant pressure and constant volume for air at this temperature is nearly

Options

A. `1.66`
B. `1.4`
C. `1.33`
D. `1.5`

Answer

B

Explanation

`v = sqrt(( gamma Rt)/(M)) rArr v = 395 m//s`
`M = 28.8 g//mol = 28.8 xx 10^(-3) kg//mol`
`T = 107^(@) C = 380 K`
`R = 8.3 J//mol K`
`gamma = ( v^(2) M)/(RT) = ((395)^(2) xx 28.8 xx 10^(-3))/(8.3 xx 380) = 1.4`