A bicycle pump with a stroke of 25 cm is used to force air into tire, through a

Question

A bicycle pump with a stroke of 25 cm is used to force air into tire, through a valve that open only when the air pressure in the pump exceeds 200 kPa. If the pump stroke begins with the pump handle fully extended, when the pump contains air at 100 kPa, how far must the pump handle be moved for air to begin entering the tire if:
a) the handle is moved so slowly that the compression process is an isothermal one
b) the handle is moved rapidly and the compression process can be described as one in which pv^y is constant, where y = cpo/cvo

Explanation / Answer

a) P1V1 =P2 V2 (as iso thermal) here, initial volume = area *25 and final volume =Area *x ( we must find x) initial pressure = 100 kPa final = 200 kPa so 100 *25*A = 200*x *A so x = 12.5 cm b) P1V1^1.4 =P2 V2^1.4 (as iso thermal) here, initial volume = area *25 and final volume =Area *x ( we must find x) initial pressure = 100 kPa final = 200 kPa so 100 *(25*A)^1.4 = 200*(x *A)^1.4 so x = 15.24 cm so piston must be moved by as distance of 9.76 cm

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