15. Equivalence of work and heat quantity

It has been proved by direct experiments that the heating of the body can occur without any heat transfer to it. This is not difficult to verify. Take two wooden sticks and rub them energetically. Putting one of the stick on your cheek afterwards will make you find that it has visibly warmed up.

On a large scale, this phenomenon was observed in 1798 by the German scientist Rumford. Drilling a gun barrel in the water led to boiling water. Where did the heat come from? Rumford rightly assumed that the water is heated in the process of drilling.

It is well known that without friction-reducing lubricant, friction forces work so hot that the bearings (for example, at the car crankshaft) melt. In modern high-speed drilling and turning machines, the heating of drills and cutters is so strong that special fluids are used to cool them.

Friction of dry pieces of wood can be used to make fire, in other words, to heat the wood to a temperature higher than flash point. It was known and could be used by prehistoric people. However, this requires a lot of art and you will hardly be able to do it yourself without a long training session.

These and similar numerous experiments show that the quantity of heat is a value which is related to work. Equivalent heating can be achieved either by transferring a certain quantity of heat \(\Delta Q\) or by performing a certain amount of work \(\Delta W\). But the work in mechanics is equal to the change of system energy. That is why the quantity of heat should be considered as a measure of the system energy change, as well as the work.

The work is a quantitative characteristic of the energy system change, followed by macroscopic movements of bodies (piston movement, shaft rotation, drill bits, etc.). Heat quantity - is a characteristic of the energy change, which is not followed by movement of bodies (gas heating in a cylinder, heat exchange in a calorimeter, etc.). That is why both the work and the quantity of heat are measured in the same units - in joules.

However, the equivalence of work and quantity of heat transferred was proved only after the experiments have shown that when the heat is received through work, the work equal to 4.19 Joules is always accompanied by receiving the quantity of heat equal to 1 Calorie. And conversely, the receiving work by the quantity of heat (for example, by using a steam engine), 1 Calorie allows you to perform work in 4.19 Joules. By doing so, it has been experimentally proved that calorie is nothing else but a heat unit of energy.

The number 4.19 j/cal (or rather 4.1868 j/cal), the so-called mechanical equivalent of heat, is the conversion factor from heat to mechanical units.

In the SI system of units, the quantity of heat is measured in joules and the specific heat capacity in joules per kilogram-degree (J/kg-degr).

The first precise measurements of the mechanical equivalent of heat were made by the Englishman Joule. One of Joule's experiments measured the quantity of heat released in calorimeter with mercury as the blades rotated, which were driven by falling weights (a weights like in Grandfather floor clocks). At the beginning and end of the experiment, the weights, blades and mercury in the calorimeter were at rest, so that the kinetic energy did not change during the experiment. Knowing the work done by the weights in motion and measuring the amount of heat released in the calorimeter when rubbing the blades against mercury, Joule found that a certain quantity of work corresponds to a strictly defined quantity of heat: a work in 4.19 J is equivalent to one calorie.