# Investigation into the Quantity of Heat

Intensity of heat reveals itself to an observer as temperature, and can be measured by a thermometer. Various clues are around that lead us to the conclusion that there is a quantity of heat separate from what we measure with a thermometer. Starting from the original views on the equilibrium of heat leads an investigator to questions. This view cannot be reconciled to phenomena such as specific and latent heat.

### A Picture of Equilibrium

It was originally thought that if two or more objects of different temperatures were placed in a closed room in which 'there is no fire, and the Sun does not shine'1, the two objects would come to equilibrium with each other and the system around them. When the system reaches equilibrium, any two equal volumes of the system will contain the same amount of heat. Also, the heat will balance out2 according to the ratios of each object's density. In other words, more heat will come out of objects that have more density. How can both of these statements be true?

### Special Heat

Joseph Black's pioneering research in the 18th Century shows us that each type of substance requires a different amount of heat, independent of its density to increase its temperature the same number of degrees. He calls this amount of heat for a substance the 'specific heat' of that substance. Specific heat is not, however, related to the density3 of the object. For instance, water has a higher specific heat than mercury. The amount of heat that is required to raise two measures of water one degree is sufficient to raise three measures of mercury one degree, but mercury is 13 times as dense as water. Therefore mercury is able to hold less heat within its greater density.

It is like the system is a cake pan. Each substance is represented by a dent in the bottom of the pan. The dent that corresponds to water is deeper than the dent for mercury, because water has a greater heat capacity4. If one were to pour a liquid into the pan, more of the liquid would be required to fill the 'water' dent than the 'mercury' dent5.

Therefore, the original picture of equilibrium of heat must change. When the objects are at equilibrium with the system and each other, any two equal volumes in the system will not contain the same amount of heat, but will contain the amount of heat particular to that object that displays an equal intensity of heat. The heat will therefore not balance out according to the ratios of each object's density, but according to the ratios of each object's specific heat.

### Hidden Heat

Another clue to understanding quantity of heat reveals itself when a substance is at its boiling or melting temperature. Take water for example. The temperature of water stays constant while it is boiling. If one boils water in an enclosed container, the water, the steam, and all of the system will remain at the same temperature until all of the water is converted into steam6. This will also occur as one melts ice. The temperature of the ice stays constant until all of the ice is converted into water. Only then does the temperature continue to rise. In both cases, the temperature of the system stays the same although heat is being added to the substance. Black calls heat that does not reveal itself as temperature 'latent heat'.

Based on these observations of heat as it relates to the boiling point and melting points of various substances, our picture of equilibrium must change again. The heat will not balance out according to each object's specific heat unless the temperature range of the experiment is such that each object stays in the same state throughout. Water, for example, can 'hide'7 extra heat after it reaches 100°C, therefore, if water and white-hot iron are the two objects, the equilibrium temperature will not balance out simply according to the ratios of their specific heat.

### Specific Specific Heat

Latent heat turns out to be a particular case of specific heat. As water is heated, the water reaches a point where it contains all of the heat that it can. At this point a thermometer in the water reads 100°C. Every quanta of heat added after this phases liquid water into vaporous water (steam). After all of the water is vaporous heat starts revealing itself again as temperature. Effectively, the specific heat capacity increases a huge amount during the time that water is boiling. In fact one can reduce this increase to a simple value for any substance. This value is the amount of heat required to boil a specific volume of the substance, which is the same as specific heat8, only applied to a particular case.

Knowing the boiling heat capacity for water, one can now take that into effect in order to predict the way that heat will balance itself out in a system. This is not simply according to specific heat, but specific heat and latent heat.

### Quantity of Heat

Based on the observations about the unique hidden and latent and specific qualities of heat, it is obvious that heat is far more complex than that which we measure with a thermometer. Heat is quantifiable. It is transferable from substance to substance, and eventually balances out to equilibrium within a system. It cannot be a liquid, because it can be 'compressed'. Although it can reveal itself through temperature, it can also be latent. A quantity of heat only reveals itself within substances. Does heat exist outside of a substance? If heat can 'hide' in boiling water, where else can it hide?

The idea of a quantity of heat separate from temperature explains why a system at boiling temperature for that substance does not increase in temperature until all of the substance is converted to vapour. Also a quantity of heat explains why different substances of the same density can contain different amounts of heat. What, then, is heat? At first glance, this seems to be an extremely elementary question whose answer focuses on a thermometer. But, given the factors of heat discussed, the answer to this question seems elusive.

1From Lectures on the Elements of Chemistry' by the 18th Century chemist Joseph Black. He means by this a closed system, one where no outside events act upon the system, not only limited to the heat from the Sun or a fire.2Or come to equilibrium by heat leaving the hotter object(s) and entering the cooler object(s).3Density=weight/volume, or amount of substance per cubic unit.4Another term for specific heat. The full term is 'specific heat capacity'.5Heat does not seem to be an actual liquid though, since more of it can be in a smaller space. Liquids are not compressible, so heat cannot be a liquid-like 'caloric', as Black and other scientists of bygone centuries believed.6Interestingly enough, any two equal amounts of volume in the system (the enclosed container) would not contain the same amount of heat, because the specific heat of a substance (in this case water) changes as the temperature of said substance changes.7Surprisingly, latent means 'Not visible or apparent'.8Specific heat is the amount of heat required to raise a certain volume of a substance one degree, while this value is the amount of heat required to raise a certain volume of a substance one degree across the boiling point.