Question

The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure
is 225 kPa. What is the temperature of the air in the tire? Assume that the
volume is constant. Make sure your answer is rounded to nearest whole
number and your final answer has the units of K.*

Answer 1

Answer : The temperature of the air in the tire is, 341 K

Explanation :

Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.

$P\propto T$

or,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

where,

$P_1$ = initial pressure = 198 kPa

$P_2$ = final pressure = 225 kPa

$T_1$ = initial temperature = $27^oC=273+27=300K$

$T_2$ = final temperature = ?

Now put all the given values in the above equation, we get:

$\frac{198kPa}{300K}=\frac{225kPa}{T_2}$

$T_2=340.9K\approx 341K$

Therefore, the temperature of the air in the tire is, 341 K