Temperature and particles related to energy

The connection between temperature and thermal energy

What is the relationship between the amount of energy in the thermal store of a warm object and the temperature of that object? In rather dated and unhelpful terms we might ask, what is the relationship between the heat energy in an object and its temperature?

To start off with, let's think about warming solids, taking care not to warm them so much that they melt and change from solid to liquid. As you warm the solid object, imagine that you keep a record of how much energy is shifted to the thermal store (no need to worry about how the energy is actually measured) and also that you measure the gradual rise in temperature of the object.

How do you expect the size of block, the quantity of energy shifted, and the temperature to be related?

Making hot chocolate

You might repeat this process, but this time thinking about warming a liquid. Imagine that you take 200 millilitre of milk from the fridge and pop in the microwave for 90 second at full power. The milk comes out just right for a hot chocolate.

You then take a further 300 ml of cold milk from the fridge to make another hot chocolate for a thirstier friend. You want to get the same drinking temperature for this greater amount of milk. It is clear that you need to put the milk in the microwave for longer to supply the extra energy for the extra liquid. In other words, the amount of energy you have to shift to achieve the same temperature depends on how much milk you have to warm.

Although not shown in this example, the quantity of energy also depends on how much you want to warm the milk. If you took the milk from a cooler fridge you would need to keep the milk in the microwave for longer to achieve the same final temperature.

Temperature and thermal energy store

Once the milk is heated up, the measured temperature does not depend on the amount of milk. For example, you might pour half of the warm milk into a separate cup. In each cup:

• The temperature of the milk is the same.
• The thermal energy stored in each cup is about half of the original (assuming not too much energy is shifted to the thermal store of the surroundings).

These observations can be linked to a particle model of the milk in each cup.

• The temperature is the same because on average the state of motion of the particles (how fast they are moving about) in both cups is the same.
• The thermal energy is halved because there is about half the number of particles moving around in each cup.

In general terms:

• The temperature of an object is related to the state of motion of its particles (the higher the temperature the faster moving are the particles).
• Temperature is termed an intensive quality since it does not depend upon the number of particles (or mass of substance) present.
• The energy in the thermal store of an object is related to the state of motion of its particles and the number of particles (a higher thermal energy follows from a larger number of faster moving particles).
• Thermal energy is an extensive quantity since it depends upon the number of particles (or mass of substance) present.