Air is drawn into a cylindrical bicycle pump at a temperature or 18.0°C and a pr

ID: 1432436 • Letter: A

Question

Air is drawn into a cylindrical bicycle pump at a temperature or 18.0°C and a pressure of 1.00 atm. The

inner diameter of the pump cylinder is 5.00 cm, and the length of the cylinder filled with air is 24.00 cm

before compression. The pump handle is then quickly pressed down, so that an adiabatic compression

of the gas occurs. Let’s assume the compression is quick enough so that the length of the air column is

decreased to 4.00 cm before the air begins to enter the tire. Assume air behaves like a diatomic ideal gas.

a) What is the initial volume of air (volume before compression)?

b) What is the volume of air just before the air enters the tire (volume after compression)?

c) What does equal for a diatomic gas?

d) What is the pressure of the air just before the air enters the tire?

e) What is the temperature of the air just before it enters the tire?

a) initial volume of air = 3.14 * 0.025 * 0.025 *0.24

= 4.71 * 10-4 m3

b) volume of air just before the air enters the tire = 3.14 * 0.025 * 0.025 *0.04

= 7.85 * 10-5 m3

c) equal for a diatomic gas = 7/5 = 1.4

d) pressure of the air just before = 1 * (4.71 * 10-4 )1.4/(7.85 * 10-5 )1.4

= 12.286 atm

e) temperature of the air just before , T1.4 = 1 * (291.15)1.4/(12.286)-0.4

= 7682.94

=> temperature of the air , T = 596.179 K

= 323.029 degree celsius

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