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?

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Assume constant volume.

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Answer 1 · 2017-05-07T12:28:59

The gases must reach a temperature of 627 °C.

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

$color(blue)(bar(ul(|color(white)(a/a) p_1/T_1=p_2/T_2color(white)(a/a)|)))" "$

We can rearrange the above formula to get

$T_2 = T_1 × p_2/p_1$

Your data are:

$p_1 = "30 kPa"$
$T_1 = "(27 + 273.15) K" = "300.15 K"$
$p_2 = "90 kPa"$
$T_2 = ?$

$T_2 = "300.15 K" × (90 color(red)(cancel(color(black)("kPa"))))/(30 color(red)(cancel(color(black)("kPa")))) = "900 K" = "627 °C"$

The new temperature is 627 °C.