Question

A cyclist gets up in Eastern Washington on a cool morning when the temperature is 5 C and inflates his bicycle tires to 95 psi. The temperature rises to 25 C over the course of the day. At 4 PM his rear tire has a blowout. His riding buddies tell him he was stupid to inflate his tires to that pressure since over the course of the day the temperature went up by a factor of five, so the pressure in his tires was nearly 500 psi. He says that's not right, that the his tire pressure only went up by a little less than 10% to 102 psi.

Who is right and why?

(A)He is, the tire pressure is approximately 102 psi

(B)He is because his tire pressure doesn't change at all

(C)His buddies are, he's lucky nobody got hurt

(D)He is, although his tire pressure is 110 psi and might be unsafe

Answer 1

PSI stands for 'pound per square inch'.

NOTE:::According to  Gay-Lussac's Law or The Pressure Temperature Law, the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. With an increase in temperature, the pressure increases.

at constant volume, number of particles inside the container should also remain constant and temperatue should be in kelvin unit.

Volume of the tire and number of particles inside it remains constant here.

Thus , whenever pressure increases tempeeature increases.

NOTE:::  The force exerted by the particles per unit of area on the container is the pressure. so when the temperature increases the pressure must also increase. Pressure is proportional to kelvin temperature, if the number of particles and the volume of the container are constant.

NOTE::: While giving directly proportional relation between the presuure and temperature , temperature should be in kelvin scale.

Who is right and why?

(A) He is, the tire pressure is approximately 102 psi

* When the temperature is 5⁰C that is 278K pressure is 95 psi.When temperature rises to 25⁰C i.e., to 298K

* While giving directly proportional relation between the presuure and temperature , temperature should be in kelvin scale. ( From Gay-Lussac's Law ).

* 10% rise means 27.8K . if it rises 10% the new temperature should be 305.8K.But in actual case the temperature rises from 278K to 298K.

* But actual rise in temperature is 20K . That rise in temperature is 7.2%. One can't consider this as little less than 10%.

According Gay-Lussac's Law rise  in pressure should also be 7.2% means new pressure should be 102 psi.

He (Cyclist ) is right.

His buddies applying Gay-Lussac's Law with celsius scale temperature.

His buddies are absolutely wrong.