Q139 / 160 · TS EAMCET 2005 · Physics

The tyre of a motor car contains air at $15^{\circ} \mathrm{C}$. If the temperature increases to $35^{\circ} \mathrm{C}$, the approximate percentage increase in pressure is (ignore to expansion of tyre)

  • Correct answer
    A
    7
  • B
    9
  • C
    11
  • D
    13

Solution

$\begin{aligned} T_1=15^{\circ} \mathrm{C} & =15+273=288 \mathrm{~K} \\ T_2 & =35^{\circ} \mathrm{C}=35+273=308 \mathrm{~K} \end{aligned}$ Volume remains constant. So, $\begin{aligned} & \frac{p_1}{T_1}=\frac{p_2}{T_2} \\ & \frac{p_1}{P_2}=\frac{T_1}{T_2} \Rightarrow \frac{p_1}{P_2}=\frac{288}{308} \\ & \frac{p_2}{p_1}=\frac{308}{288} \end{aligned}$ $\begin{aligned} \% \text { increase in pressure } & =\frac{p_2-p_1}{p_1} \times 100 \\ & =\frac{308-288}{288} \times 100 \\ & \approx 7 \% \end{aligned}$

Hence, the correct answer is option: 'A'.

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