Quantity of Heat

Excerpts

• Quantity of Heat

  It was, in general, customary to take as the unit of heat that quantity which must be added to $1~\Unit{gr.}$ of water to raise its temperature from $0°$ C. to $1°$ C. (zero calorie).

• Quantity of Heat

  This, in general, varies with temperature, but very slowly for most substances. It is usually permissible to put the specific heat at a certain temperature equal to the mean specific heat of an adjoining interval of moderate size.

• Quantity of Heat

  A gas at $0°$ and atmospheric pressure can be brought to a state where its temperature is $100°$ and its pressure $10$ atmospheres, either by heating to $100°$ under constant pressure, and then compressing at constant temperature; or by compressing isothermally to $10$ atmospheres, and then heating isopiestically to $100°$; or, finally, by compressing and heating simultaneously or alternately in a variety of ways.

• Quantity of Heat

  It is reckoned *positive* when heat is set free or developed, *i.e.* given out by the body (exothermal processes); *negative*, when heat is absorbed, or rendered latent, *i.e.* taken up by the body (endothermal processes).

• Quantity of Heat

  Latent heat, as in the case of specific heat, is best referred, not to unit mass, but to molecular or atomic weight.

• Quantity of Heat

  If we plunge a piece of iron and a piece of lead, both of equal weight and at the same temperature ($100°$ C.), into two precisely similar vessels containing equal quantities of water at $0°$ C., we find that, after thermal equilibrium has been established in each case, the vessel containing the iron has increased in temperature much more than that containing the lead. Conversely, a quantity of water at $100°$ is cooled to a much lower temperature by a piece of iron at $0°$, than by an equal weight of lead at the same temperature.

• Quantity of Heat

  It would be absurd to define the heat contained in a body of given temperature, density, etc., as the number of calories absorbed by the body in its passage from some normal state into its present state, for the quantity thus defined would assume different values according to the way in which the change was effected.

• Quantity of Heat

  To explain the rise of temperature which takes place notwithstanding, it was necessary to make the assumption that compression and friction so diminish the body’s heat capacity, that the same amount of heat now produces a higher temperature, just as, for example, a moist sponge appears more moist if compressed, although the quantity of liquid in the sponge remains the same.

• Quantity of Heat

  Each one of these experimental results would by itself be sufficient to disprove the hypothesis of the indestructibility of heat, and to overthrow the older theory.

• Quantity of Heat

  That the heat capacities of different substances should be referred to unit mass is quite arbitrary. It arises from the fact that quantities of matter can be most easily compared by weighing them.

• Quantity of Heat

  It cannot be claimed that this law is rigorously true, since the heat capacity depends on the molecular constitution, as in the case of carbon, and on the state of aggregation, as in the case of mercury, as well as on the temperature.

• Quantity of Heat

  At such temperatures the heat absorbed no longer affects the entire body, but only one of the parts into which it has split; and it no longer serves to increase the temperature, but simply to alter the state of aggregation, *i.e.* to melt, evaporate, or sublime.

Equations

• Quantity of Heat

  \frac{Q}{\Delta\theta} = c_{m}.

  The mean specific heat (mean heat capacity) of 1 gram of a substance is the heat it receives divided by the corresponding increase of temperature between the initial and final temperatures of the process.

• Quantity of Heat

  \frac{Q}{d\theta} = c.

  The specific heat of a substance at temperature theta is the quantity of heat received divided by the infinitely small increase of temperature.

Problems

No exercises in this chapter.