Air (a diatomic ideal gas) at 27.08C and atmosphericpressure is drawn into a bicycle

Chapter 21, Problem 32

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Air (a diatomic ideal gas) at 27.08C and atmosphericpressure is drawn into a bicycle pump (see the chapteropeningphoto on page 626) that has a cylinder withan inner diameter of 2.50 cm and length 50.0 cm.The downstroke adiabatically compresses the air,which reaches a gauge pressure of 8.00 3 105 Pa beforeentering the tire. We wish to investigate the temperatureincrease of the pump. (a) What is the initial volumeof the air in the pump? (b) What is the numberof moles of air in the pump? (c) What is the absolute pressure of the compressed air? (d) What is the volumeof the compressed air? (e) What is the temperature ofthe compressed air? (f) What is the increase in internalenergy of the gas during the compression? WhatIf? The pump is made of steel that is 2.00 mm thick.Assume 4.00 cm of the cylinders length is allowed tocome to thermal equilibrium with the air. (g) What isthe volume of steel in this 4.00-cm length? (h) What isthe mass of steel in this 4.00-cm length? (i) Assume thepump is compressed once. After the adiabatic expansion,conduction results in the energy increase in part(f) being shared between the gas and the 4.00-cmlength of steel. What will be the increase in temperatureof the steel after one compression?