Question

A car starts out when the air temperature is 288 K. The air pressure in the tires is 460 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming the volume remains constant?

(A) 476 kPa
(B) 498 kPa
(C) 488 kPa
(D) 563 kPa
(E) 512 kPa

Answer 1

(A) 476 kPa

Step-by-step explanation:

If the volume remains constant, the ideal gas law says:

P/T=constant

so: P1/T1=P2/T2

P2=P1*T2/T1=460*298/288=476KPa

Answer 2

A. The final pressure at the tire would be 476 kPa

Step-by-step explanation:

Since the volume is constant the ideal gas equation would be used to obtain the final pressure at the tire.

Given

the initial temperature
`T_(1)` = 288 K

the initial pressure
`P_(1)` = 460 k Pa

the final temperature
`T_(2)` = 298 K

the final pressure
`P_(2)` = ?

Using the ideal gas equation;

PV = nRT

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

Making
`P_(2)` the subject formula

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

`P_(2)` = (460 x 298) / 288

`P_(2)` = 475.972 kPa

`P_(2)` ≈ 476 kPa

Therefore the final pressure at the tire would be 476 kPa