Answer to Question #1507 in Mechanics | Relativity for mike
Question #1507
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.
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.
Expert's answer
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 -Patm = 862.9-101.3 = 761.66 kPa
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 -Patm = 862.9-101.3 = 761.66 kPa
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