Answer:
900 K
Explanation:
Recall the ideal gas law:
[tex]\displaystyle PV = nRT[/tex]
Because only pressure and temperature is changing, we can rearrange the equation as follows:
[tex]\displaystyle \frac{P}{T} = \frac{nR}{V}[/tex]
The right-hand side stays constant. Therefore:
[tex]\displaystyle \frac{P_1}{T_1} = \frac{P_2}{T_2}[/tex]
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:
[tex]\displaystyle \begin{aligned} \frac{(30\text{ atm})}{(300\text{ K})} & = \frac{(90\text{ atm})}{T_2} \\ \\ T_2 & = 900\text{ K}\end{aligned}[/tex]
Hence, the temperature must be reach 900 K.
