Heat

Chapter contents: Chapter 8: Thermal Physics

We have defined work as force times distance and learned that work done on an object changes its kinetic energy. We have also seen that temperature is proportional to the (average) kinetic energy of atoms and molecules. We say that a thermal system has a certain internal energy: its internal energy is higher if the temperature is higher. If two objects at different temperatures are brought in contact with each other, energy is transferred from the hotter to the colder object until equilibrium is reached and the bodies reach thermal equilibrium (i.e., they are at the same temperature). No work is done by either object, because no force acts through a distance. The transfer of energy is caused by the temperature difference, and ceases once the temperatures are equal. These observations lead to the following definition of heat: Heat is the spontaneous transfer of energy due to a temperature difference.

Heat is often confused with temperature. For example, we may say the heat was unbearable, when we actually mean that the temperature was high. Heat is a form of energy, whereas temperature is not. The misconception arises because we are sensitive to the flow of heat, rather than the temperature.

Heat transfers energy, so its SI unit is the joule (J). The calorie (cal) is another unit of energy, historically based on the energy needed to raise the temperature of 1 g of water by 1°C. Because water’s specific heat varies with temperature, several calorie conventions developed. This textbook uses the thermochemical calorie, defined as exactly 4.184 J. A kilocalorie (kcal) equals 1000 calories, or exactly 4184 J. Food Calories (Cal), sometimes called “big calories,” are kilocalories: 1 Cal = 1 kcal.

In figure a there is a soft drink can and an ice cube placed on a surface at a distance from each other. The temperatures of the can and the ice cube are T one and T two, respectively, where T one is not equal to T two. In figure b, the soft drink can and the ice cube are placed in contact on the surface. The temperature of both is T prime. — **Figure 8.4.1.** In figure (a) the soft drink and the ice have different temperatures, $T_{1}$ and $T_{2}$ , and are not in thermal equilibrium. In figure (b), when the soft drink and ice are allowed to interact, energy is transferred until they reach the same temperature $T'$ , achieving equilibrium. Heat transfer occurs due to the difference in temperatures. In fact, since the soft drink and ice are both in contact with the surrounding air and bench, the equilibrium temperature will be the same for both.

Mechanical Equivalent of Heat

It is also possible to change the temperature of a substance by doing work. Work can transfer energy into or out of a system. This realization helped establish the fact that heat is a form of energy. James Prescott Joule (1818–1889) performed many experiments to establish the mechanical equivalent of heat—the work needed to produce the same effects as heat transfer. In terms of the units used for these two terms, the thermochemical convention gives the exact conversion

1.000 kcal = 4184 J

(8.4.1)

We consider this equation as the conversion between two different units of energy.

In the figure, there is a can of known volume full of water and fitted with a thermometer at the top. On both sides of the can two blocks of weight W each hang from cords. The cords pass over two pulleys and wind around a cylindrical roller. There is a handle attached with the roller to rotate it manually. Submerged in the water are some paddles attached to a vertical rod attached at the bottom of the roller. When the lever is rotated, the paddles move inside the water. — **Figure 8.4.2.** Schematic depiction of Joule’s experiment that established the equivalence of heat and work.

The figure above shows one of Joule’s most famous experimental setups for demonstrating the mechanical equivalent of heat. It demonstrated that work and heat can produce the same effects, and helped establish the principle of conservation of energy. Gravitational potential energy (PE) (work done by the gravitational force) is converted into kinetic energy (KE), and then randomized by viscosity and turbulence into increased average kinetic energy of atoms and molecules in the system, producing a temperature increase. His contributions to the field of thermodynamics were so significant that the SI unit of energy was named after him.

Heat added or removed from a system changes its internal energy and thus its temperature. Such a temperature increase is observed while cooking. However, adding heat does not necessarily increase the temperature. An example is melting of ice; that is, when a substance changes from one phase to another. Work done on the system or by the system can also change the internal energy of the system. Joule demonstrated that the temperature of a system can be increased by stirring. If an ice cube is rubbed against a rough surface, work is done by the frictional force. A system has a well-defined internal energy, but we cannot say that it has a certain “heat content” or “work content”. We use the phrase “heat transfer” to emphasize its nature.

Exercise

Check Your Understanding

Two samples (A and B) of the same substance are kept in a lab. Someone adds 10 kilojoules (kJ) of heat to one sample, while 10 kJ of work is done on the other sample. How can you tell to which sample the heat was added?

Solution

Heat and work both change the internal energy of the substance. However, the properties of the sample only depend on the internal energy so that it is impossible to tell whether heat was added to sample A or B.

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