# On a cold winter morning when the temperature is -13°C, the air pressure in an automobile tire is 1.5 atm. If the volume does not change, what is the pressure after the tire has warmed to 15°C?

Apr 9, 2017

Pressure will be $1.662$ atm

#### Explanation:

When volume does not change

${P}_{i} / {T}_{i} = {P}_{f} / {T}_{f}$, where temperature is in kelvins

As initial temperature is $- {13}^{\circ} C = {\left(273 - 13\right)}^{\circ} K$ and initial pressure is $1.5 a t m$, at ${15}^{\circ} C = {\left(273 + 15\right)}^{\circ} K$, pressure will be given by

$\frac{1.5}{260} = {P}_{f} / 288$

and ${P}_{f} = \frac{288 \times 1.5}{260} = 1.662$ atm