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.

Step-by-step 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.

`(P_(1))/(T_(1)) = (P_(2))/(T_(2))`

Substitute the values into above formula as follows.

`(P_(1))/(T_(1)) = (P_(2))/(T_(2))\\(500 kPa)/(298 K) = (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.