Answer to Question #1507 in Mechanics | Relativity for mike

Question

The tire on a bicycle is filled with air to a
gauge pressure of 658 kPa at 20 degrees C.
What is the gauge pressure in the tire after
a ride on a hot day when the tire air temperature is 60 degrees C? (Assume constant volume and a
constant atmospheric pressure of 101.3 kPa.)
Answer in units of kPa.

Answer 1

For the constant volume we use Gay-Lussac's law:
P₁/T₁= P₂/T₂

Thus P₂ = P₁T₂/T₁
For our case P₁ = 658 + 101.3 = 759.3 kPa (absolute pressure); T₁ = 20C = 293 K; T₂ = 60C = 333 K.
P₂ = 759.3*333/293 = 862.9 kPa.

The gauge pressure is P = P₂ -P_atm = 862.9-101.3 = 761.66 kPa