Chapter 16 Temperature and Heat - HCC Learning Web

Chapter 16

Temperature and Heat

16-1 Temperature and the Zeroth Law of Thermodynamics

Definition of heat:

Heat is the energy transferred between objects because of a temperature difference.

Objects are in thermal contact if heat can flow between them.

When the transfer of heat between objects in thermal contact ceases, they are in thermal equilibrium.


The Zeroth law of Thermodynamics

If bodies A and B are each in thermal equilibrium with a third body T, then A and B are in thermal equilibrium with each other.


The zeroth law of thermodynamics:

If object A is in thermal equilibrium with object B, and object C is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact.

That is, temperature is the only factor that determines whether two objects in thermal contact are in thermal equilibrium or not.

16-2 Temperature Scales

The Celsius scale:

Water freezes at 0° Celsius.

Water boils at 100° Celsius.

The Fahrenheit scale:

Water freezes at 32° Fahrenheit .

Water boils at 212° Fahrenheit .

Converting between Celsius and Fahrenheit:


Converting between Fahrenheit and Celsius :


The pressure in a gas is proportional to its temperature. The proportionality constant is different for different gases, but they all reach zero pressure at the same temperature, which we call absolute zero:


The Kelvin scale is similar to the Celsius scale, except that the Kelvin scale has its zero at absolute zero.

Conversion between a Celsius temperature and a Kelvin temperature:


The three temperature scales compared:

16-3 Thermal Expansion

Most substances expand when heated; the change in length or volume is typically proportional to the change in temperature.

The proportionality constant is called the coefficient of linear expansion.

Thermal ExpansionWhen the temperature of an object is raised, the body usually exhibit “thermal expansion”. With the added thermal energy, the atoms can move a bit farther from one another than usual, against the spring-like interatomic forces that hold every solid together.)

The atoms in the metal move farther apart than those in the glass, which makes a metal object expand more than a glass object.


Some typical coefficients of thermal expansion:


A bimetallic strip consists of two metals of different coefficients of thermal expansion, Aand B in the figure. It will bend when heated or cooled.


The expansion of an area of a flat substance is derived from the linear expansion in both directions:

Holes expand as well:


The change in volume of a solid is also derived from the linear expansion:

For liquids and gases, only the coefficient of volume expansion is defined:

Thermal Expansion, Volume Expansion

If all dimensions of a solid expand with temperature, the volume of that solid must also expand. For liquids, volume expansion is the only meaningful expansion parameter.

If the temperature of a solid or liquid whose volume is V is increased by an amount ΔT, the increase in volume is found to be

where β is the coefficient of volume expansion of the solid or liquid. The coefficients of volume expansion and linear expansion for a solid are related by


Some typical coefficients of volume expansion:

Example, Thermal Expansion of Volume:

Thermal Expansion, Anomalous Expansion of Water

The most common liquid, water, does not behave like other liquids. Above about 4°C, water expands as the temperature rises, as we would expect.

Between 0 and about 4°C, however, water contracts with increasing temperature. Thus, at about 4°C, the density of water passes through a maximum.

At all other temperatures, the density of water is less than this maximum value.

Thus the surface of a pond freezes while the lower water is still liquid.


Water also expands when it is heated, except when it is close to freezing; it actually expands when cooling from 4° C to 0° C. This is why ice floats and frozen bottles burst.

16-4 Heat and Mechanical WorkExperimental work has shown that heat is another form of energy.

James Joule used a device similar to this one to measure the mechanical equivalent of heat:

16-4 Heat and Mechanical Work

One kilocalorie (kcal) is defined as the amount of heat needed to raise the temperature of 1 kg of water from 14.5° C to 15.5° C.

Through experiments such as Joule’s, it was possible to find the mechanical equivalent:

16-4 Heat and Mechanical Work

Another unit of heat is the British thermal unit (Btu). This is the energy required to heat 1 lb of water from 63° F to 64° F.

Temperature and Heat

Heat is the energy transferred between a system and its environment because of a temperature difference that exists between them.

16-5 Heat CapacityThe heat capacity of an object is the amount of heat added to it divided by its rise in temperature:

Q is positive if ΔT is positive; that is, if heat is added to a system.

Q is negative if ΔT is negative; that is, if heat is removed from a system.

16-5 Specific Heats

The heat capacity of an object depends on its mass. A quantity which is a property only of the material is the specific heat:

16-5 Specific Heats

Here are some specific heats of various materials:

16-6 Conduction, Convection, and Radiation

Conduction, convection, and radiation are three ways that heat can be exchanged.

Conduction is the flow of heat directly through a physical material.

16-6 Conduction

Experimentally, it is found that the amount of heat Q that flows through a rod:

• increases proportionally to the cross-sectional area A

• increases proportionally to the temperature difference from one end to the other

• increases steadily with time

• decreases with the length of the rod

16-6 Conduction

Combining, we find:

The constant k is called the thermal conductivity of the rod.

16-6 Conduction, Convection, and Radiation

Some typical thermal conductivities:

Substances with high thermal conductivities are good conductors of heat; those with low thermal conductivities are good insulators.

Heat Transfer Mechanisms: Convection

In convection, energy transfer occurs when a fluid, such as air or water, comes in contact with an object whose temperature is higher than that of the fluid.

The temperature of the part of the fluid that is in contact with the hot object increases, and (in most cases) that fluid expands and thus becomes less dense.

The expanded fluid is now lighter than the surrounding cooler fluid, and the buoyant forces cause it to rise.

Some of the surrounding cooler fluid then flows so as to take the place of the rising warmer fluid, and the process can then continue.

16-6 Convection

Convection is the flow of fluid due to a difference in temperatures, such as warm air rising. The fluid “carries” the heat with it as it moves.

16-6 Radiation

All objects give off energy in the form of radiation, as electromagnetic waves – infrared, visible light, ultraviolet – which, unlike conduction and convection, can transport heat through a vacuum.

Objects that are hot enough will glow – first red, then yellow, white, and blue. Objects at body temperature radiate in the infrared, and can be seen with night vision binoculars.

16-6 Radiation

The amount of energy radiated by an object due to its temperature is proportional to its surface area and also to the fourth (!) power of its temperature.

It also depends on the emissivity, which is a number between 0 and 1 that indicates how effective a radiator the object is; a perfect radiator would have an emissivity of 1.

16-6 Radiation

This behavior is contained in the Stefan-Boltzmann law:

Here, e is the emissivity, and σ is the Stefan-Boltzmann constant:

Heat Transfer Mechanisms: Radiation

In radiation, an object and its environment can exchange energy as heat via electromagnetic waves. Energy transferred in this way is called thermal radiation.

The rate Prad at which an object emits energy via electromagnetic radiation depends on the object’s surface area A and the temperature T of that area in K, and is given by:

Here σ =5.6704 x10-8 W/m2 K4 is called the Stefan–Boltzmann constant, and ε is the emissivity.

If the rate at which an object absorbs energy via thermal radiation from its environment is Pabs, then the object’s net rate Pnet of energy exchange due to thermal radiation is:

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Chapter 16 Temperature and Heat - HCC Learning Web