Air (a diatomic ideal gas) at 30.0°C and atmospheric pressure is drawn into a bicycle pump that has a cylinder with an inner diameter of 2.50 cm and length 70 cm. The down stroke adiabatically compresses the air, which reaches a gauge pressure of 800 kPa before entering the tire. (a) Determine the volume of the compressed air.

Question

m3
(b) Determine the temperature of the compressed air.
K
(c) The pump is made of steel and has an inner wall that is 1.80 mm thick. Assume that 14.70 cm of the cylinder's length is allowed to come to thermal equilibrium with the air. What will be the increase in wall temperature?
K

I tried using the pv=nrt formuala rearaanged but i am confused on how the thickness and length play a part?

Answer 1

a) For the adiabatic compression, use the formula P V^1.4 = constant to get the final volume

b) Once you know the final volume V2, use the perfect gas law to get T2, before heat is lost to the cylinder.

c) Use the heat capacity of the steel to determine how much the gas temperature drops at equilibrium

Answer 2

im sorry i tried using PV^1.4=22.3l but this was not the right answer could you explain further the equation for a.