We often have the experience of pumping air into bicycle tyre using hand pump. Consider the air inside the pump as a thermodynamic system having volume V at atmospheric pressure and room temperature, `27^(@)C`. Assume that the nozzle of the tyre is blocked and you push the pump to a volume `1//4` of V. Calculate the final temperature of air in the pump? (For air, since the nozzle is blocked air will not flow into tyre and it can be treated as an adiabatic compression). Take `gamma` for air `= 1.4`

Explanation

Here, the process is adiabatic compression. The volume is given and temperature is to be found. We can use the equation.
`T_(i)V_(i)^(gamma-1)`
`T_(i)=300K(273+27^(@)C=300K)`
`V_(i)=V&V_(f)=(V)/(4)`
`T_(f)=T_(i)((V_(i))/(V_(f)))^(gamma-1)=300K xx4^(1.4-1)=300Kxx1.741`
`T_(2)~~522K or 249^(@)C`
This temperature is higher than the boiling point of water. So it is very dangerous to touch the nozzle of blocked pump when you pump air.