Question

A car tire has a pressure of 30 psi at a temperature of 27ºC. Calculate the extremes of pressure  caused by temperatures ranging from -20.0ºC on a cold winter day to 50.0ºC while being driven  on a hot summer day.

Answer 1

According to Gay-Lussac's Law, the pressure of a given mass of a gas is directly proportional to its absolute temperature, so long as volume is kept constant.

Thus,

P$\alpha$T

P = T x constant

P = Tk

$\dfrac{P}{T} = k$

Therefore,

$\dfrac{P1}{T1} = \dfrac{P2}{T2}$

Solving for P2 becomes

$P2 =\dfrac{P1T2}{T1}$ T1=(27+273)K = 300K

P1 = 30psi

(i) During winter when T2 = (-20 + 273)K = 253K

P2 $=\dfrac{30psi x253K}{300K} = 25.3psi$

(ii) During winter when T2=(50 + 273)K = 323K

P2 $=\dfrac{30psi x 323K}{300K} = 32.3psi$