Question

# Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 200∘C. During the day the temperature rises to 400∘C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

A

209 kPa

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B

285 kPa

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C

355 kPa

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D

392 kPa

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Solution

## The correct option is B 392 kPa The ideal gas equation relates the state variables as: PV = nRT. Assuming no leakage in the tyre, it is safe to assume that the number of moles of air, n, has not changed in the process. Thus, the fraction n=(pvRT) will be constant. Also, if the initial volume is V, the final volume will be [102100×V], or 1.02V. Denoting the final pressure as Pf, we can write - n=[Pf×1.02 VR×40]=[200×VR×20] ⇒Pf=(200×4020×1.02) kPa=392 kPa.

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