Air is pumped into an automobile tube upto a pressure of 200 kPa in the morning when the air temperature is 22°C. During the day, temperature rises to 42°C and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately

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206 kPa

212 kPa

200 kPa

209 kPa

answer is B.

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Detailed Solution

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}} Here, P_{1} = 200 kPa$

$\begin{array}{l} T_{1} = 22^{\circ} C = 295 K T_{2} = 42^{\circ} C = 315 K \\ V_{2} = V_{1} + \frac{2}{100} V_{1} = 1 .02 V_{1} \\ ∴ P_{2} = \frac{200 \times 315 V_{1}}{295 \times 1 .02 V_{1}} = 209 .37 kPa \end{array}$

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