q = C ∆T and q = mc ∆T
where do those formulae come from? can you explain intuitively?
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Heat capacity is the amount of energy you have to put in to an object to get its temperature to go up by one degree.
So the standard measurement is joules per kelvin (how many joules to make it go up by one degree kelvin.
C is the specific heat capacity of the object (the amount of energy required to raise the temperature of 1 gram by 1 degree K)
∆T is the change in temperature.
q is the amount of heat lost by a particular sample
[khan academy have an excellent unit about it](https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:thermodynamics/x2eef969c74e0d802:heat-capacity-and-calorimetry/v/heat-capacity)
Q = mcΔT is something we derived through experimentation. We know how much energy we put into a material, and we can measure its mass and temperature, and they relate such that Q~mΔT, but there’s some constant in there depending on the material, which is c.
Heat capacity or specific heat is that constant. All ot means is that some materials are better at holding energy in the form of heat than others. If I have something cold with a high specific heat and something hot with a low specific heat, and I touch them together, the low specific heat thing is going to cool down a lot faster than the high specific heat one heats up. That’s because the energy leaving one has to be the same energy entering the other, but the one with the high specific heat has so much more capacity for that heat.
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