Question

The total pressure in an 12.2 l automobile tire is 41.0 psi at 15.0 ∘c. how much does the pressure in the tire rise if it warms to a temperature of 32.0 ∘c and the volume remains at 12.2 l?.

Answer 1

As, volume is constant here, we can apply Gay-Lussac's law. It states that the pressure exerted on the sides of a container by an ideal gas is directly proportional to its absolute temperature for a given mass and constant volume. That is,

`(P_(1) )/(P_(2) )=(T_(1) )/(T_(2) )`

We have, P₁ = 41 psi

T₁= 15°C=15+273.15 = 288.15 K

T₂=32°C= 32+273.15 = 305.15 K

Substituting values,

`(41)/(P_(2))= (288.15)/(305.15)`

P₂=
`(41)/(0.95)`

P₂=43.15 psi

The pressure in the tire would rise to 43.15 psi if it warms to a temperature of 32.0° C.