Is heat directly proportional to mass


The uninhibited viewer is forced to believe that a warmer body gives off "something" while it is cooling, which the cooler body absorbs while it is warming up. In order to have a formative name for it, we refer to this "something" as, after Black Amount of heat. In this expression, the body with the higher temperature gives off an amount of heat to the one with the lower one. The loss of heat is considered to be the cause of the cooling of one body, its absorption by the other body as the cause of its heating. This newly introduced "quantity concept" of heat, which is supposed to stand alongside the "intensity concept" temperature, only gains real meaning because we can measure the "amount of heat" and specify it numerically.

Here, too, the quantity of heat can only be measured by measuring its effects, and for the time being we only know the changes in temperature of such effects. So we will set the amount of heat Δq absorbed (or released) by a body proportional to its temperature change ΔT before and after absorption (or release): Δq ~ ΔT; or with the proportionality constant C:

Δq = C ΔT,

where C is the heat capacity. Since the change in the amount of heat Δq is proportional to the mass of the body, we can introduce the specific heat capacity c and we get:

Δq = c * m * ΔT

Since this is always about Temperature differences the equation also applies to the Celsius temperature t. In this equation, c turns out to be a material-dependent factor. But it contains two unknowns, namely Δq and c. If we knew or knew how to measure the specific heat capacity c, we could also measure the amount of heat Δq and vice versa.

In the past, the factor c was set arbitrarily for any substance in a certain temperature range. It was agreed that water between 14.5 and 15.5 ° C should have the unit of specific heat capacity. With this determination, the unit of the amount of heat was defined at the same time and thus the possibility of measuring any amount of heat was gained. The unit of the amount of heat then results as follows: If c is set equal to the unit and m = 1 g, by heating 1 g of water from 14.5 ° C to 15.5 ° C under normal pressure, so that the temperature difference Δt = 1 degree is, then Δq becomes equal to the unit of the amount of heat. It was called 1 calorie (1 cal).

The mass here represents the amount of substance. However, it is often useful to relate the heat capacity directly to the amount of substance. One then speaks of the molar heat capacity C.m. Between Cm and c there is a connection

C.m = M * c

where M is the molar mass. When setting the unit of heat quantity as described, one is bound to the material properties of the water. However, there is a tendency to do as far as possible without material properties when defining units.

But then what is the true nature of heat? Since it can be generated e.g. through friction, i.e. through work, the idea that it is a form of energy is obvious. If this is the case, one must expect that a given work, when it is converted into heat, generates a certain amount of heat every time, regardless of the way in which the conversion of work into heat takes place, that is to say regardless of the type of process used as well as the physical and chemical properties of the substances used. In other words: there must be a fixed numerical relationship between the heat previously measured in calories and the work used to generate it, which is measured in joules.

Fig. 1: Joules apparatus for determining the mechanical heat equivalent. The sinking weight does work, E = mgh, in the water of the container, whereby the energy E can be determined via the change in temperature.
J.P. Joule provided this evidence through systematic experiments between 1842 and 1850. The train of thought of one of his experiments is as follows: A body of mass m, which is lifted to height h, has a potential energy mgh. When this body sinks, it does work, and this is converted into heat in the following way: The sinking body moves a paddle wheel, which rotates under strong friction in a liquid (e.g. mercury). If the body M has sunk down, the energy mgh has disappeared, but instead heat has appeared in the liquid. If their mass is m, their specific heat capacity c, their temperature increase ΔT, then the amount of heat generated is equal to mcΔT. Now the quotient has to be mgh/mcΔTif heat is a form of energy, it must be constant and independent of the experimental conditions. Today applies:

1 calorie (cal) = 4.1868 joules (J)

If you don't have to deal with these numbers often, you hardly have a "feel" for how much a calorie, a newton meter or a joule is. The easiest way to estimate one kilowatt hour from the consumption of electrical energy. It is both rewarding and surprising to make simple comparisons, either through calculations or through simple measurements. The kinetic energy of a pistol bullet is 100 J. On the other hand, a match emits a thermal energy of 1000 J.

J / gK J / gKJ / molKJ / molKJ / molK
Mercury vapor0,10471,66670,062820,80812,5608,428
Hydrogen chloride0,81221,41610,573629,64721,0268,621
Carbon dioxide0,84571,33570,623836,92828,4288,500
Nitrous oxide0,83741,29030,64936,84428,4708,374

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