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A car tyre is slowly pumped up to a pressure of 2atm in an environment at 15C. at this...

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A car tyre is slowly pumped up to a pressure of 2atm in an environment at 15C. at this point it bursts. Assuming the sudden expansion of the air (a mix of O2 and N2) that was inside the tyre to be adiabatic what its temperature is after the burst.

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A car tyre is slowly pumped up to a pressure of 2 atm in an environment at 15 C. When the tyre bursts, the pressure of the gas pumped in to the tyre is equal to 1 atm. It is assumed that the volume of the gas remains the same momentarily. In an adiabatic process there is no exchange of heat to the environment.

Use the ideal gas law: PV = n*R*T

Initially 2*V = n*R*15 ...(1)

After the explosion, 1*V = n*R*T' ...(2)

(2)/(1)

=> 1/2 = T'/15

=> T' = 7.5

The required temperature of the gas is 7.5 C

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