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

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?

Explanation / Answer

Thermodynamic processes adiabatic

a) calculate the volume

The body is a cylinder

V = A L

A = (d/2)2

Data

d = 5 cm = 5 10-2m

L = 24 cm = 24 10-2 m

Vo = ( 5 10-2 /2)224 10-2

Vo = 471.23 10-6m³

b) Lf = 24 -4 = 20 cm = 20 10-2 m

Vf = ( 5 10-2/2)220 10-2

Vf = 392.70 10-6m

c) diatomic gass

= 7/5

d)

expression for the pressure in an adiabatic process is

(P/Po) (V/Vo)= 1

P = (Vo/V)Po

P= ( 471.23/392.70) 7/5 1.013 105

P = 1.29 Atm

e) To calculate the temperature we use the equation of ideal gases

PV = nRT

Tf = Pf Vf /n R

To = Po Vo / nR

Tf/To = Pf/Po Vf/Vo

Tf = Pf/Po Vf/Vo To

Tf = 1.29/1 392.7/471.23 18

Tf = 19.35 C

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