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

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212 kPa

209 kPa

206 kPa

200 KPa

answer is B.

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Detailed Solution

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ (As no. of moles remains same)

Given, $P_{1} = 200 Kpa, V_{1} = V,$

$T_{1} = 273 + 22 = 295 K,$

$V_{2} = V + 0.02 V, T_{2} = 273 + 42 = 315 K$

$\Rightarrow P_{2} = \frac{200 \times 315}{295 \times 1.02} \approx 209 Kpa$

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