You fill your tires with air on a cold morning (-7) degrees Celsius to 216 kPa gauge pressure, then drive into a 31 degrees Celsius desert. a) Assuming the volume of air in the tires remains constant, whats the new gauge pressure? b) What would be the gauge pressure if the volume of air had expanded by 5% ?

Question

You fill your tires with air on a cold morning (-7) degrees Celsius  to 216 kPa  gauge pressure, then drive into a 31 degrees Celsius desert. a) Assuming the volume of air in the tires remains constant, whats the new gauge pressure? b) What would be the gauge pressure if the volume of air had expanded by 5% ?

mos1635 · Answer

a)
assuming ideal gas
P1*V=n*R*T1
P2*V=n*R*T2
so
P1/P2=T1/T2
T1=-7+273
T2=36+273
b) 
P1*V=n*R*T1
P2*1.05V=n*R*T2