Question

5. The gases in a hair spray can are at a temperature of 37 °cand a pressure of 5.6 atm. If the gases in the can reach apressure of 4.4 atm, the can will explode. To what temperaturemust the gases be raised in order for the can to explode? (Donot try this at home)

Answer 1

243.69 K

Step-by-step explanation

Given:

Initial temperature, T₁ = 37 °C = (37 + 273.15 K) = 310.15 K

Initial pressure, P₁ = 5.6 atm

Final pressure, P₂ = 4.4 atm

What to find:

The temperature to which the gases must be raised in order for the can to explode.

Step-by-step solution:

According to Amonton's Law, it states that the pressure of an ideal gas varies directly with the absolute temperature when the volume of the sample is held constant.

The final temperature of the gas can be calculated using Amonton's law formula given by

`(P_1)/(T_1)=(P_2)/(T_2)`

Putting the values of the given parameters into the equation:

`\begin{gathered} (5.6atm)/(310.15K)=(4.4atm)/(T_2) \\ \\ T_2=(4.4atm*310.15K)/(5.6atm) \\ \\ T_2=243.69\text{ }K \end{gathered}`

The temperature to which the gases must be raised in order for the can to explode is 243.69 K