# Which Physical Quantity Deserves the Name “Quantity of Heat”?

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## Abstract

**:**

## 1. Introduction

## 2. Profile of a Physical Quantity Amount of Heat

- Heat is contained in a body. It is distributed within the body. Two bodies, one of which contains 3 units of heat and the other 2 units, together contain 5 units;
- If heat is added to a body, its temperature usually rises. It may happen that the temperature does not rise despite the supply of heat, for example when water is boiling. However, now the water evaporates. Steam must therefore contain more heat than liquid water of the same temperature (scalding with steam is known to be worse than with boiling water). One can also increase the temperature of a gas by compressing it, and thereby compressing the heat;
- Heat can pass or flow from one body to another. If there is a suitable connection between two bodies, heat passes or flows “by itself” from the warmer to the colder one;
- Heat is generated in a flame and in many other chemical reactions, as well as by friction and by electric currents; it is not taken away from another system in these processes, but is generated anew.

## 3. The Candidates

- $Q$
- $H$
- ${E}_{\mathrm{therm}}$
- $S$

“If one looks for an appropriate name for S, then one could say the quantity $S$ to be the transformation content of the body, similarly as the quantity $U$ is said to be the heat and work content of the body. However, since I think it is better to choose the names of quantities, which are important in science, from the old languages, so that they can be applied unchanged in all the new languages, I propose to call the quantity $S$ according to the Greek word ητροπη, the transformation, the entropy of the body.”

#### 3.1. The Quantity $Q$

#### 3.1.1. Definition and Use

“The physical quantity heat describes a part of the energy absorbed or supplied by a system. The remaining part is work.”

“Heat is energy in transfer to or from a system A to a system B by a mechanism other than work or transfer of matter.”

“The change of the energy due to the energy transport as a result of a purely thermal interaction is called heat.”

#### 3.1.2. Which Criteria of the Profile Are Met

#### 3.2. The Quantity $H$

#### 3.2.1. Definition and Use

“When a process occurs at constant pressure, the heat released or absorbed is equal to the change in enthalpy. Enthalpy ($H$) is the sum of the internal energy ($U$) and the product of pressure and volume ($pV$) given by the equation:$$H=U+pV.{}^{\u2033}$$

“Enthalpy $H$ is a thermodynamic state variable. It is a designation for the amount of heat given off or absorbed by a reaction. It is measured in kJ (kilojoules). One cannot measure the enthalpy of a state, but only the difference between two states.”

#### 3.2.2. Which Criteria of the Profile Are Met

#### 3.3. The Quantity ${E}_{\mathrm{therm}}$

#### 3.3.1. Definition and Use

“The potential and the kinetic energy of the particles together are also called thermal energy.”

“The total energy of a thermodynamic system, which consists of thermal energy (potential and kinetic energy of the particles), of chemical energy and nuclear energy, is the internal energy $U$.”

“Thermal energy refers to the energy contained within a system that is responsible for its temperature. Heat is the flow of thermal energy.”

#### 3.3.2. Which Criteria of the Profile Are Met

#### 3.4. The Quantity $S$

#### 3.4.1. Definition and Use

#### 3.4.2. Which Criteria of the Profile Are Met

## 4. How It Came about That the Simple Meaning of Entropy Was Not Recognized—A Drama in Three Acts

#### 4.1. Act One: The Old Heat and Its Decline

#### 4.1.1. Joseph Black—The First Measure for the Amount of Heat

“If, for example, we have one pound of water in one vessel, and two pounds in another, and these two quantities of water are equally hot, as examined by the thermometer, it is evident, that the two pounds must contain twice the quantity of heat that is contained in one pound. Undoubtedly, we can suppose that a cubical inch of iron may contain more heat than a cubical inch of wood, heated to the same degree; and we cannot avoid being convinced of this by daily experience.”

“The heat producible by the strong friction of solid bodies, occurs often in some parts of heavy machinery, when proper care is not taken to diminish that friction as much as possible…”

#### 4.1.2. Sadi Carnot—Heat Engine and Water Wheel

“We find it useless to explain here what is the quantity of caloric or quantity of heat (for we use the two expressions indifferently), nor to describe how these quantities are measured by the calorimeter. Nor will we explain what latent heat, degree of temperature, specific heat, etc. is. The reader must become familiar with these expressions by studying elementary treatises on physics or chemistry.”

“According to the notions established so far, the motive power of heat can fairly be compared to that of a waterfall: both have a maximum that cannot be exceeded, whatever on the one hand the machine used to receive the action of water, and whatever on the other hand is the substance employed to receive the action of heat.The motive power of a waterfall depends on its height and the amount of liquid; the motive power of heat also depends on the quantity of caloric employed, and what might be called, what we shall call the height of its fall, that is to say, the difference in temperature of the bodies between which is the exchange of caloric takes place.”

#### 4.1.3. Joule, Mayer, Helmholtz—Heat Becomes Energy

**v**is the velocity and

**p**the momentum.

“According to Carnot’s conception, the body would have received on the path AB an amount of heat … from a heat reservoir ${\mathrm{R}}_{1}$ … of temperature ${\vartheta}_{1}$ as it would have released on the path CD to a heat reservoir ${\mathrm{R}}_{0}$ of temperature ${\vartheta}_{0}$… He concluded that heat could perform external work if it was transferred in unchanged quantity from bodies of higher temperature (the reservoir ${\mathrm{R}}_{1}$) to one (${\mathrm{R}}_{0}$) of lower temperature, as if it had a state of greater elastic tension at higher temperature and expanded when it passed to lower temperature, whereby the elastic tension of the heat substance is converted into external work. Carnot’s consideration is correct insofar as with this gain in work a certain quantum of heat must necessarily pass from a warmer to a colder body. Yet, it is wrong insofar as the working body mediating the heat transfer does not give off as much heat at the lower temperature ${\vartheta}_{0}$ as it has absorbed at ${\vartheta}_{1}$; it gives off less heat, and the difference is equivalent to the external work gained.”

“The material theory of heat must necessarily consider the quantity of the heat substance as constant.”

#### 4.1.4. Clausius—Introduction of the Entropy

#### 4.2. Act Two: Resurrection without Consequence

#### 4.2.1. Ostwald: Entropy as the Resurrected Caloric

“However, the quantity of the thermodynamic theory, which could be compared with the amount of water, is still completely unfamiliar to the general public. It has received the scientific name entropy and plays a role corresponding to its meaning in the theory of thermal phenomena. However, in school and thus in the knowledge of the average-educated, the use of this quantity has not yet gained acceptance and so the information here must be that it really is comparable to the amount of water in so far as its amount does not change as it passes through the (ideal) machine.”

#### 4.2.2. Callendar: Entropy for the Schoolboy

“Finally, in 1865, when its importance was more fully recognised, Clausius … gave it the name of ‘entropy’, and defined it as the integral of $\mathrm{d}Q/T$. Such a definition appeals to the mathematician only. In justice to Carnot, it should be called caloric, and defined directly by his equation $W=AQ\left(T\u2013{T}_{0}\right)$, which any schoolboy could understand. Even the mathematician would gain by thinking of caloric as a fluid, like electricity, capable of being generated by friction or other irreversible processes.”

#### 4.2.3. Jaumann: The Local Balance Equation

#### 4.2.4. The Preliminary End

#### 4.3. Act Three: Second Resurrection

## 5. Consequences for Teaching

#### 5.1. Integration into the Physics Canon

- Electricity is about electric charge and its currents;
- Mechanics is about momentum and its currents (“forces”);
- Thermodynamics is about entropy and its currents;
- Chemistry is about the amount of substance and its currents, and about reactions.

#### 5.2. Surrogate Quantities and Substitute Constructions

#### 5.2.1. Energy Dissipation

#### 5.2.2. Energy Loss

#### 5.2.3. The Principle of Minimum Energy

#### 5.3. University Students’ Problems with Thermodynamics

#### 5.4. Teaching Practice

- Among two bodies of the same temperature, differing only in size, the larger one contains more entropy;
- Entropy flows spontaneously from warm to cold. If one wants it to flow from cold to warm, one needs a heat pump;
- Entropy can be generated in many different ways, but it cannot be annihilated. When teaching, one realizes that this statement, which seems so transcendent to the physicist, can be concluded solely from the everyday experience of the students;
- With the help of a cryogenic machine (a heat pump) one can extract entropy from a body, whereby its temperature decreases. However, one does not succeed in achieving a temperature below −273 °C. The reason for this is that the body contains no more entropy. We introduce the absolute temperature scale;
- Entropy transport by conduction and by convection is discussed.

## 6. Conclusions

“In any case, it is a hard work to develop a new scientific view in a more or less known area and to consider the old phenomena in a new light; it is as if one had to describe a familiar content in a new language, which one first has to learn for this purpose. What a wonder, if one tries again and again to keep the way of expression of the old language and to apply the new one only where it cannot be otherwise, because the old one had been inadequate.”

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Extensive Quantity | Current | Intensive Quantity | Energy Current | |
---|---|---|---|---|

electricity | $Q$ | $I$ | $\varphi $ | $P=U\xb7I$ |

mechanics | $p$ | $F$ | $v$ | $P=v\xb7F$ |

thermodynamics | $S$ | ${I}_{S}$ | $T$ | $P=T\xb7{I}_{S}$ |

chemistry | $n$ | ${I}_{n}$ | $\mu $ | $P=\mu \xb7{I}_{n}$ |

Find it Interesting | Feel Competent | |
---|---|---|

mechanics | 4/10 | 9/10 |

thermodynamics | 4/10 | 2/10 |

modern physics | 9/10 | 3/10 |

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Herrmann, F.; Pohlig, M.
Which Physical Quantity Deserves the Name “Quantity of Heat”? *Entropy* **2021**, *23*, 1078.
https://doi.org/10.3390/e23081078

**AMA Style**

Herrmann F, Pohlig M.
Which Physical Quantity Deserves the Name “Quantity of Heat”? *Entropy*. 2021; 23(8):1078.
https://doi.org/10.3390/e23081078

**Chicago/Turabian Style**

Herrmann, Friedrich, and Michael Pohlig.
2021. "Which Physical Quantity Deserves the Name “Quantity of Heat”?" *Entropy* 23, no. 8: 1078.
https://doi.org/10.3390/e23081078