The guage pressure in an automobile tire reads 32 psi in
thewinter at 273 k. the guage reads the difference between thetire
pressure and the atmospheric pressure (14. psi). inother words, the
tire pressure is the guage reading plus 14.7psi. if the same tire
were used in the summer at 316 k and noair had leaked from the
tire, what would be the tire guage readingin the summer?

Tire gauge reading = 40.0 psi

Explanation:

We can solve this question by making use of Gay Lusac law which says that the pressure of a gas is directly proportional to the absolute temperature (K) of the gas:

P₁/T₁ = P₂/T₂   ⇒ P₂ = (P₁/T₁) x T₂

Notice that we have to assume the volume of the tire remains constant which is a reasonable assumption.

P₁ = (32 +14.7) psi = 46.7 psi

T₁ = 273 K

P₂ = ?

T₂ = 316 K

P₂ = (46.7 psi/ 273 K )  x 316 K = 54.06 psi

Gauge reading = 54.06 psi - 14.07 psi = 40.0 psi psi