# The gases in a hair spray can are at a temperature of 27 C and a pressure of 30 kPa. If the gases in the can reach a pressure 90 kPa, the can will explode. To what temperature must the gases be raised in order for the can to explode?

## Assume constant volume.

May 7, 2017

The gases must reach a temperature of 627 °C.

#### Explanation:

Since the volume is constant but the pressure and temperature are changing, this is an example of Gay-Lussac's Law:

$\textcolor{b l u e}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} {p}_{1} / {T}_{1} = {p}_{2} / {T}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

We can rearrange the above formula to get

T_2 = T_1 × p_2/p_1

${p}_{1} = \text{30 kPa}$
${T}_{1} = \text{(27 + 273.15) K" = "300.15 K}$
${p}_{2} = \text{90 kPa}$
T_2 = ?
${T}_{2} = \text{300.15 K" × (90 color(red)(cancel(color(black)("kPa"))))/(30 color(red)(cancel(color(black)("kPa")))) = "900 K" = "627 °C}$