An automobile tire at 30°C has a pressure of 3.00 atm. Temperature decreases to -5°C. Assume that there is no volume change in the tire.

What is the new pressure of the tire after the temperature change?

P₂ = 2.7 atm

Explanation:

Given data:

Initial temperature = 30°C

Initial pressure = 3.00 atm

Final temperature = -5°C

Final pressure = ?

Solution:

Initial temperature = 30°C = 30 + 273 = 303 K

Final temperature = -5°C = -5 + 273 = 268 K

According to Gay-Lussac Law,

The pressure of given amount of a gas is directly proportional to its temperature at constant volume and number of moles.

Mathematical relationship:

P₁/T₁ = P₂/T₂

Now we will put the values in formula:

3.0 atm / 303 K = P₂/268 K

P₂ = 3.0 atm × 268 K / 303 K

P₂ = 804 atm. K /293 K

P₂ = 2.7 atm

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