Question

A car tyre is filled with nitrogen gas at $35psi$ at $27{}^{°}C$. It will burst if pressure exceeds $40psi$. Find the temperature in${}^{°}C$ at which the car tyre will burst?

Answer 1

Step 1: Given data

Initial pressure in tyre, $P_1=35psi$

Final pressure in tyre, $P_2=40psi$

Initial temperature, $T_1=27{}^{°}C=300K$

Step 2: Find the temperature at which tyre will burst

Assuming that no. of moles of $N_2$ gas and volume of tyre remains constant and pressure is changed by changing temperature.

Using,

$$\begin{gathered} \frac{P}{T}=cons\tan t \\ \frac{P_1}{T_1}=\frac{P_2}{T_2} \\ {T}_2=\frac{P_2\times T_1}{P_1} \\ \Rightarrow T_2=\frac{40psi\times 300K}{35psi} \\ \approx 343K \end{gathered}$$

Step 3: Find the temperature in${}^{°}C$

Temperature in ${}^{°}C$ is calculated by

$T_2-273=70{}^{°}C$

Hence, the temperature in${}^{°}C$ at which the car tyre will burst is $70{}^{°}C$.