Boyle's Law describes a behavior without positing the mechanism.
What does it mean for a gas to heat up? Is the quantity of heat energy increasing, or the temperature?
A thermometer generally measures the temperature of molecules adjacent to the thermometer, which is a function of the amplitude of those molecules' vibration. More molecules within a given space increases the heat capacity, and the total heat energy represented by a temperature of the total quantity of molecules, but the temperature is a function of the average heat energy per individual molecule.
The temperature increase described by Boyle's law is a consequence of the work required to compress a gas—somewhere there has to be a compressor imparting kinetic energy to individual atoms.
Think of it this way, you have two containers of heat energy represented by 1L of an ideal gas at 1 atmosphere and 20°C. If you magically transported the contents of both containers into a single 1L container, and they continued to express a temperature of 20°C, you would have twice as much stuff, and contain twice as much heat energy in 1L. If on the other hand you had twice as much stuff and a higher temperature, then you would have increased the total amount of energy present in the universe.
The temperature comes from the extra energy put into the system to compress the gas rather than expressly from the density of the heat energy.
What does it mean for a gas to heat up? Is the quantity of heat energy increasing, or the temperature?
A thermometer generally measures the temperature of molecules adjacent to the thermometer, which is a function of the amplitude of those molecules' vibration. More molecules within a given space increases the heat capacity, and the total heat energy represented by a temperature of the total quantity of molecules, but the temperature is a function of the average heat energy per individual molecule.
The temperature increase described by Boyle's law is a consequence of the work required to compress a gas—somewhere there has to be a compressor imparting kinetic energy to individual atoms.
Think of it this way, you have two containers of heat energy represented by 1L of an ideal gas at 1 atmosphere and 20°C. If you magically transported the contents of both containers into a single 1L container, and they continued to express a temperature of 20°C, you would have twice as much stuff, and contain twice as much heat energy in 1L. If on the other hand you had twice as much stuff and a higher temperature, then you would have increased the total amount of energy present in the universe.
The temperature comes from the extra energy put into the system to compress the gas rather than expressly from the density of the heat energy.