# The pressure in a bicycle tire is 1.34 atm at 33.0°C. At what temperature will the pressure inside the tire be 1.60 atm if volume is constant?

Dec 22, 2015

The temperature will be 366 K.

#### Explanation:

This is an example of Gay-Lussac's law in which the pressure and Kelvin temperature are directly proportional at constant volume. The equation to use is ${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$.

${P}_{1} = \text{1.34 atm}$
${T}_{1} = \text{33.0"^"o""C"+273.15="306.2 K}$
${P}_{2} = \text{1.60 atm}$
${T}_{2} = \text{???}$

Solution
Rearrange the equation to isolate ${T}_{2}$ and solve.
${P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}$

${T}_{2} = \frac{{P}_{2} {T}_{1}}{P} _ 1$

${T}_{2} = \left(1.60 \cancel{\text{atm"xx306.2"K")/(1.34cancel"atm}}\right)$

${T}_{2} = \text{366 K}$