Question

A tyre pumped to a pressure of `6 atmosphere` bursts suddenly. Calculate the temperature of escaping air. Given initial room temperature is `15^(@)C` and gamma for air is 1.4`.

Answer 1

Correct Answer - `176.2K`
`P_(1)= 6 atm. P_(2)= 1 atm`
`T_(1)= 273+15= 288K, T_(2)= ? gamma= 1.4`
From `P_(2)^((1-gamma))T_(2)^(gamma)= P_(1)^((1-gamma))T_(1)^(gamma)`
`T_(2)= T_(1)((P_(1))/(P_(2)))^((1-gamma)//(gamma))=288(6/1)^(((1-1.4))/(1.4))`
`=288xx6^(-2//7)= 172.6K`