You are inflating a bicycle tire with a hand-powered pump like the one shown. Wh

Question

You are inflating a bicycle tire with a hand-powered pump like the one shown. When the handle is fully extended, the volume of air inside the pump is 100 cm3. At the bottom of the stroke, when the air is fully compressed, the volume has been reduced to 9.7 cm3. The gas is mostly diatomic, with = 1.4.

Just for fun, you push down on the handle very slowly, so that the gas compresses in an isothermal manner.

As you compress the gas inside the pump, its temperature will _______

The pressure inside the pump is obviously greater than it was before compression. The new pressure is times _______higher than the original pressure.

Of course, no one wants to have to inflate a bike tire that slowly. Now you push the handle down quickly and forcefully, compressing the gas in an adiabatic manner.

As you compress the gas inside the pump, its temperature will _________.

The pressure inside the pump is obviously greater than it was before compression. The new pressure is _____ times higher than the original pressure

Explanation / Answer

initial volume V1 = 100 cm^3

final volume = V2 = 9.7 cm^3

for isothermal process temperature is constant

P1*V1 = P2*V2

P2 = P1*(V1/V2)

P2 = P1(100/9.7) = 10.3 P1

As you compress the gas inside the pump, its temperature will __remains same_____

The pressure inside the pump is obviously greater than it was before compression. The new pressure is times ___10.3____higher than the original pressure.

compressing the gas in an adiabatic manner.

P1*v1^r = P2*v2^r

r = 1.4

P2/P1 = (v1/v2)^r

P2/P1 = (100/9.7)^1.4 = 26.21

As you compress the gas inside the pump, its temperature will ___increase______.

The new pressure is __26.21___ times higher than the original pressure

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