# 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:

P

Thus P

For our case P

P

The gauge pressure is P = P

P

_{1}/T_{1}= P_{2}/T_{2}Thus P

_{2}= P_{1}T_{2}/T_{1}For our case P

_{1}= 658 + 101.3 = 759.3 kPa (absolute pressure); T_{1}= 20C = 293 K; T_{2}= 60C = 333 K.P

_{2}= 759.3*333/293 = 862.9 kPa.The gauge pressure is P = P

_{2}-P_{atm}= 862.9-101.3 = 761.66 kPaNeed a fast expert's response?

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## Comments

Assignment Expert22.08.13, 16:56You're welcome. We are glad to be helpful.

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Jake19.08.13, 23:42Thanks so much for the help!!

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