A car tyre is pressurized with nitrogen to 35 text psi at 27^ circ text C . The tyre is rated to burst if the internal pressure exceeds 40 text psi . At what temperature (in ^ circ text C ) will the tyre likely burst?

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EEJ MAIN Chemistry QUESTION #7177

Question 1

A car tyre is pressurized with nitrogen to $35 \text{ psi}$ at $27^{\circ}\text{C}$. The tyre is rated to burst if the internal pressure exceeds $40 \text{ psi}$. At what temperature (in $^{\circ}\text{C}$) will the tyre likely burst?

$50^{\circ}\text{C}$
$60^{\circ}\text{C}$
$70^{\circ}\text{C}$✔️
$80^{\circ}\text{C}$

Correct Answer Explanation

According to Gay-Lussac's Law ($P/T = \text{constant}$):

$P_{1} = 35 \text{ psi}$, $T_{1} = 27 + 273 = 300 \text{ K}$
$P_{2} = 40 \text{ psi}$, $T_{2} = ?$
$35/300 = 40/T_{2}$
$T_{2} = (40 \times 300) / 35 \approx 342.8 \text{ K}$
Converting to Celsius: $342.8 - 273 = 69.8^{\circ}\text{C} \approx 70^{\circ}\text{C}$

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