Question

The gasses in a hair spray can are at temperature 300k and a pressure of 30 atm, it

Answer 1

Answer:

900 K

Explanation:

Recall the ideal gas law:

$\displaystyle PV = nRT$

Because only pressure and temperature is changing, we can rearrange the equation as follows:
$\displaystyle \frac{P}{T} = \frac{nR}{V}$

The right-hand side stays constant. Therefore:

$\displaystyle \frac{P_1}{T_1} = \frac{P_2}{T_2}$

The can explodes at a pressure of 90 atm. The current temperature and pressure is 300 K and 30 atm, respectively.

Substitute and solve for T₂:

$\displaystyle \begin{aligned} \frac{(30\text{ atm})}{(300\text{ K})} & = \frac{(90\text{ atm})}{T_2} \\ \\ T_2 & = 900\text{ K}\end{aligned}$

Hence, the temperature must be reach 900 K.