Question

The air pressure in the tires of an automobile is adjusted to 27.0 psi at a gas station in San Diego, where the air temperature is 68°F. The air in the tires is at the same temperature as the atmosphere. The automobile is then driven east along a hot desert highway, and the temperature inside the tires reaches 138 °F. What is the pressure in the tires?

Answer 1

Gay-Lussac's law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant.

Mathematically, it can be written as:

${\displaystyle {\frac {P}{T}}=k}$ .

where:

P is the pressure of the gas,

T is the temperature of the gas (measured in kelvins),

k is a constant.

For comparing the same substance under two different sets of conditions, the law can be written as:

P1/T1 = P2/T2. Or P1T2 = P2T1

Or, P2 = P1T2 /T1

In this question, P1 = 27.0psi , T1 = 68°F = 293.15K,. [ (°F-32) ×5/9 +273.15 =K ], T2= 138°F = 332.039K . To find P2.

So, P2 = 27× 332.039 / 293.15 = 30.58 psi

Therefore, pressure in the tire is 30.58psi