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Answer :
Final answer:
To calculate the temperature at which the pressure in the hairspray can reaches 90 lbs/in2, Gay-Lussac's law is used. This law indicates that the pressure of a gas is directly proportional to the temperature, given constant volume. After converting the initial and final temperatures to Kelvin, the equation yields the required temperature for the can to explode.
Explanation:
The student is asking about the relationship between gas pressure and temperature inside a container (in this case, a hairspray can) when volume is held constant. This is a typical application of the Gay-Lussac's law in thermodynamics, which states that the pressure of a gas is directly proportional to its temperature when the volume is constant.
To find the temperature at which the pressure in the hairspray can reaches 90 lbs/in2, assuming the initial temperature is 27℃ and the initial pressure is 30 lbs/in2, you can set up the equation based on Gay-Lussac's law: (P1/T1) = (P2/T2), where P1 is the initial pressure, T1 is the initial temperature in Kelvin, P2 is the final pressure, and T2 is the final temperature in Kelvin.
The temperatures must be converted to Kelvin by adding 273.15 to the Celsius value. Therefore, the equation becomes:
(30 lbs/in2/ (27 + 273.15)) = (90 lbs/in2/T2)
Solving for T2 gives us the temperature at which the can will explode.
Remember, when working with gases and pressurized containers, safety precautions are paramount. The examples provided offer insight into why certain labels and warnings are included with such containers.
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