Question

The gauge pressure in your car tires is 2.50×10^5N/m22.50×10^5⁢N/m^2 at a temperature of 35.0ºC when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to -40.0ºC?

Answer 1

Answer: $3.30\times 10^5N/m^2$

Explanation:

Gay-Lussac's Law: This law states that pressure is directly proportional to the temperature of the gas at constant volume and number of moles.

$P\propto T$     (At constant volume and number of moles)

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

where,

$P_1$ = initial pressure of gas  = $2.50\times 10^5N/m^2$

$P_2$ = final pressure of gas  = ?

$T_1$ = initial temperature of gas  = $35^0C=(35+273)K=308K$

$T_2$ = final temperature of gas  =  $-40^0C=(-40+273)K=233K$

${2.50\times 10^5N/m^2\times 308}={P_2\times 233}$

$P_2=3.30\times 10^5N/m^2$

Therefore, the final gauge pressure in the car tires is $3.30\times 10^5N/m^2$