If an “empty” aerosol can at 1 atm and 20 °C is thrown into a campfire so that it reaches a temperature of 500 °C, what will be the final pressure inside the can?

To solve this problem, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature, if the volume and the amount of gas are kept constant. This relationship is expressed by the formula P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

Here are the steps to solve the problem:

1. Convert all temperatures to Kelvin. The Kelvin scale starts at absolute zero, which is -273.15°C. So, to convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature. Therefore, T1 = 20°C + 273.15 = 293.15 K and T2 = 500°C + 273.15 = 773.15 K.

2. Substitute the known values into the formula. We know that P1 = 1 atm, T1 = 293.15 K, and T2 = 773.15 K. We want to find P2. So, the formula becomes 1 atm / 293.15 K = P2 / 773.15 K.

3. Solve for P2. To do this, we multiply both sides of the equation by 773.15 K. This gives us P2 = (1 atm / 293.15 K) * 773.15 K.

4. Calculate the value. P2 = (1 atm / 293.15 K) * 773.15 K = 2.64 atm.

So, the final pressure inside the can will be approximately 2.64 atmospheres.