Answer :
Final answer:
To find the internal pressure of a CO₂ fire extinguisher after a temperature increase, apply the combined gas law using the temperatures in Kelvin and the initial pressure given. The formula P2 = P1 * (T2/T1) calculates the final pressure when P1 is the initial pressure, and T1 and T2 are the initial and final temperatures in Kelvin.
Explanation:
The student is asking how to calculate the internal pressure of a CO₂ fire extinguisher when its temperature increases due to being left in a hot environment.
This kind of problem is a direct application of the Ideal Gas Law, which states that PV=nRT (where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin).
Since the volume and amount of gas in the extinguisher remain constant, this situation simplifies to the combined gas law P1/T1 = P2/T2, which allows us to find the final pressure (P2) after a temperature change.
To calculate the final pressure (P2), we must first convert the temperatures to Kelvin, which means adding 273.15 to each Celsius temperature.
The initial temperature (T1) is 21°C + 273.15 = 294.15 K, and the final temperature (T2) after the increase is 71.1°C + 273.15 = 344.25 K.
Using the formula P2 = P1 * (T2/T1), where P1 is the initial pressure of 20.0 atm, we can find the final pressure.
Replacing with the given values, the calculation will be P2 = 20.0 atm * (344.25 K / 294.15 K).
After performing the division and multiplication, the resultant pressure (P2) can be expressed to the appropriate number of significant figures based on the initial conditions provided.
