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?

Question

Assume constant volume.

42606 views around the world

You can reuse this answer
Creative Commons License

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.