Question

Air (γ = 1.4) is pumped at 2 atm pressure in a motor tyre at 20°C. If the tyre suddenly bursts, what would be the temperature of the air coming out of the tyre? Neglect any mixing with the atmospheric air.

Answer 1

The temperature of the air coming out of the tyre is $240.3 \mathrm{K}$

Explanation:

Step 1:

Given data,

In case of  air, $\gamma=1.4$

Initial air temperature, $T_{1}=20^{\circ} \mathrm{C}=293 \mathrm{K}$

Initial pressure, $P_{1}=2 a t m$

Final pressure, $P_{2}=1 \text { atm }$

Step 2:

The tyre burst is a adiabatic process. For a given adiabatic method,

$P_{1}^{1-\gamma} \times T_{1}^{1-\gamma}=P^{1-\gamma} \times T_{2}^{\gamma}$

$(2)^{1-1.4} \times(293)^{1.4}=(1)^{1-1.4} \times T_{2}^{1.4}$

$(2)^{-0.4} \times(293)^{1.4}=T_{2}^{1.4}$

$2153.78=T_{2}^{1.4}$

$T_{2}=(2153.78)^{1 / 1.4}$

$=240.3 \mathrm{K}$