A long tube contains air pressure of `1 atm` and a temperature of `59^(@) 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 distances `16 cm , 49.2 cm and 82.4 cm` from open end. Molar mass of air is `28.8 g//mol`.
Ratio of heat capacities at constant pressure and constant volume for air at `59^(@) C` is

Options

A. `1.4`
B. `1.152`
C. `1.60`
D. `2`

Answer

B

Explanation

`v = sqrt((gamma RT)/(M))`
`M = 28.8 g//mol = 28.8 xx 10^(-3) kg//mol`
`T = 332 K`
`R = 8.3 J//K mol`
`gamma = (v^(2) M)/(RT) = ((332)^(2) xx 28.8 xx 10^(-3))/(8.3 xx 332) = 1.152`