Question

The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure

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