The difference between heat and temperature

In boiling water, three bodies of equal mass made of different materials (e.g., Al, Pb, and Fe) are heated to the same temperature. Then, quickly transfer the hot bodies into containers filled with room temperature water. The transferred bodies will heat the cold water in the containers to varying temperatures.
Although all three bodies are at the same temperature (100°), they did not transfer the same amount of heat Q due to differences in their heat capacities.

The heat capacity of the body is the amount of heat that the body needs to receive in order to raise its temperature by 1°.
And the specific heat normalizes that heat per 1 kg of mass.

Objects or substances with a low heat capacity heat up quickly even after a short period of exposure to a heat source, whereas those with a relatively high heat capacity require a long period of exposure to the heat source for their temperature to change even slightly.

In everyday life, we experience heat capacity usually while waiting for water to boil. So let's calculate how long it takes, for example, in a 900 W microwave oven to boil 1 liter of cold water with an initial temperature of 13 °C? If we ignore the losses, let's assume that all the energy of the oven is converted into heat. Then the power of the oven P is multiplied by the heating time t, all the energy that passes into the water as heat Q.

Now we can extract the time t:

So if the waiting time for water to boil seems long, it is because water has a large heat capacity.

We will easily show this with an experiment in which we will subject air and water to the flame of a match.

We will only need two or more balloons and a match or a lighter, and maybe a candle. We will inflate the children's balloon so that it is well tightened. Then we will bring the flame of a match or lighter to the balloon. BOOM!!! The balloon will immediately burst with a loud bang. And this is nothing unexpected, because most people know about this phenomenon from experience. But in the second part of the experiment, we will show that the balloon can withstand long-term heating with an open flame, which is not known to everyone.

Now we will fill the second balloon with cold tap water. It will elongate due to the weight of the water. If we bring an open flame to a balloon filled in this way, it will not burst, even after prolonged heating. To make the experiment more dramatic for the audience, we can hold the balloon together with the lit flame above the head, while being completely sure that it will not leak. After all, if it leaks, it will be fun.

How is that possible?

Since the temperature change ΔT is inversely proportional to the heat capacity c a body with a higher capacity will have a smaller temperature change for the same amount of supplied heat Q.

The first thermal property that distinguishes water and air in the described experiment is the heat capacity c which for water is c = 4187 J·kg^-1·K^-1, while the capacity of air is four times smaller. That's why we can supply heat to water for a long time without its temperature rising just a little.

Another important property is thermal conductivity λ. The unit of measurement for thermal conductivity is watt per kelvin and meter (W/mK). For water it is λ = 0,57 W·K^-1·m^-1, while for air the conductivity is λ = 0,025 W·K^-1·m^-1.

Water therefore has about 22 times better thermal conductivity. From the above data, it is obvious that the same flame will transfer heat from the membrane of the balloon to the water faster, so due to its capacity and conductivity, the temperature of the membrane of the balloon will rise only slightly. While, on the other hand, the air in the balloon neither receives heat (due to its low capacity), nor does it remove heat from the rubber membrane. That's why the heat of the flame is absorbed by the wall of the balloon and it bursts immediately.