Question

A car starts out when the air temperature is 298 K and the absolute (total) air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 315 K. What is the pressure in the tires at that point, assuming their volume does not change

Answer 1

Answer: The pressure in the tires at that point is 528.52 kPa.

Explanation:

Given: $T_{1}$ = 500 K,          $P_{1}$ = 500 kPa

$T_{2}$ = 315 K,              $P_{2}$ = ?

According to Gay-Lussac's law, at constant volume the pressure of a gas is directly proportional to temperature.

Formula used to calculate the pressure is as follows.

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$

Substitute the values into above formula as follows.

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}\\\frac{500 kPa}{298 K} = \frac{P_{2}}{315 K}\\P_{2} = 528.52 kPa$

Thus, we can conclude that the pressure in the tires at that point is 528.52 kPa.