Difference between temperature and heat

It is becoming very difficult for me to understand the difference between temperature and heat.

1. Heat exchange is related to as exchange of matter + energy.

2. Heat is related as total kinetic energy of molecules. Translational + vibrational + rotational.

Now, I can kind of relate energy here. For exchange of matter, it’s like if put a ice cube (less kinetic energy ) into fire (high kinetic energy ). Then there is exchange of kinetic energy or both will try to make their kinetic energy equal by one reducing it and the other increasing it.

1. Temperature is related to as average kinetic energy of moles from the equipartition theorem.

Now, we know as temperature of room increases, heat of the room also increases.

I am not able to think or find any difference between the two.

• An evocative example: put a cube of plastic and an ice cube in the freezer, after a while they'll be the same temperature. Then grab them with your hands. The plastic cube will heat up much, much faster, because its specific heat is much lower - and so, it needs much less heat (from your hand) to reach thermal equilibrium with your hand. Same initial and final temperatures, very different heat exchange.
– SF.
Jun 7 '21 at 10:14
• @SF. Thank you very much. I got it. Jun 7 '21 at 10:15
• another example: consider the atoms of the material are all little cars.. the temperature is how fast they're going, and the heat is the combination of how fast and how heavy they are. A prius going 100 on the highway is the same "temperature" but has less "heat" than a truck going the same speed. I like this example because it's not too different to imagine in the mind as what kinetic theory (Boltzmann) is trying to explain. Jun 7 '21 at 21:22
• One correction. You say "Heat exchange is related to as exchange of matter + energy". Heat transfer is related to energy. Mass transfer (think extracting coffee essence from ground coffee beans into water) has very similar behavior, but has nothing to do with energy transfer. Heat transfer is driven by temperature differences. Mass transfer is driving by concentration differences (and kinda-sorta similar to how electricity transfer (current) is driven by voltage differences and liquid flow by pressure differences) Jun 7 '21 at 21:44

In engineering terms heat (energy) and temperature are two different things.

One (of many) real life examples is the kitchen stove. When you turn on the kitchen, (and leave it at a set point), the kitchen will provide thermal energy (heat) at a constant rate. However if you put a pan onto the kitchen stove you will see that its temperature rises initially and then reaches a certain point.

In the above scenario, you see that thermal energy is accumulated into the frying pan. That accumulation causes the temperature to rise.

To wrap this up, in this context :

• Heat (or heat energy, or heat flux): is the thermal energy that moves from one system to another (or from one part of the system to another). In nature, heat flow from hotter to cooler parts.
• Temperature: is a measure of the thermal energy which is accumulated in a system. That thermal energy is "stored" as kinetic energy of the molecules in the system.

Some differences between energy and heat

Quality Heat Temperature
Is it a type of energy Yes No
Does it describe the state of the system No yes
Does it transfer from one system to another yes No
Can it be measured absolutely No yes
Does it determine the rate of energy exchange No yes
Is it a system property No yes

Additionally, heat transfer can result (actually most of the times does) in temperature change (there are exceptions like phase change).

• Ok. Thanks a lot. It is much clearer now. Jun 7 '21 at 6:39
• +1 But temperature is a material property? This is a very strange usage of "material property". Temperature would typically not be considered a material property, but an independent variable ( en.wikipedia.org/wiki/List_of_materials_properties ). You can ask "What is the thermal conductivity of pure iron?" or "What is the Curie temperature of pure iron?" This answer might vary depending on temperature and pressure, but I don't think anyone would ever ask "What is the temperature of pure iron?". Jun 7 '21 at 21:44
• @watermolecule thanks for that. It slipped through the net. I was intending to replace material with system but I forgot to delete the original. I will do that in a while. Jun 7 '21 at 22:13

A little example:

• Water has a specific heat capacity (SHC) of 4.2 kJ.kg-1.K-1.
• I have a 2.1 kW electric kettle.
• $$\Delta T = \frac {P \cdot t}{m \cdot SHC}$$ where $$\Delta T$$ is the temperature rise, $$P$$ is power (kW), $$t$$ is time and $$m$$ is mass (kg).
• If I run the kettle for 60 s I will put $$2.2 \times 60 = 132 \ \text{kJ}$$ (energy) into the water.
• If I have 1 L of water the temperature rise will be $$\Delta T = \frac {2.1 \cdot 60}{1 \cdot 4.2} = 30 ^\mathrm{o}\text C$$
• If I have 2 L of water the temperature rise will be $$\Delta T = \frac {2.1 \cdot 60}{2 \cdot 4.2} = 15 ^\mathrm{o}\text C$$

You can see here that we have added the same amount of heat into both masses of water but have raised the temperature by different amounts because the additional heat is distributed through a greater mass in the larger volume of water and so the resultant temperature rise is lower.

• Thank you very much. Very interesting too. Jun 7 '21 at 10:15

Temperature is an intensity , heat is a quantity.

Keep adding heat to water when it is at 100 deg C causes a phase change but no more temperature change.

• Is it like heat is just exchange of kinetic energy by means of matter at constant temperature which causes change of phase ? Jun 7 '21 at 6:28