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## Acknowledgments

This presentation is based on and includes content derived from the following OER resource:

University Physics Volume 2

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## Temperature

Temperature is defined operationally as the quantity measured by a

thermometer. Later, when we study the kinetic theory of gases, we will see that temperature is a measure of the average energies of the particles in a system.

Heat transfer is the movement of energy from one place to another as a

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## Thermal Equilibrium

Two objects with the same temperature do not exchange temperature, and are said to be in thermal equilibrium.

The zeroth law of thermodynamics states that if system 𝐴𝐴 is in equilibrium with system 𝐵𝐵, and system 𝐵𝐵 is in contact with system 𝐶𝐶, then system 𝐴𝐴 is in equilibrium with system 𝐶𝐶.

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## Thermometers

Any property of an object that depends on temperature can be utilized to make a thermometer. Such properties include volume, color, and emission of infrared radiation.

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## Temperature Scales

Temperature readings are commonly given on one of three scales:

The unit for the Fahrenheit scale is the degree Fahrenheit (℉). The freezing point of water is 32℉ and the boiling point is 212℉.

The unit for the Celsius scale is the degree Celsius (℃). The freezing point of water is 0℃ and the boiling point of water is 100℃.

The Kelvin scale is an absolute temperature scale, meaning its zero point is equal to absolute zero, the temperature at which the average kinetic energy of molecules is zero. The freezing and boiling points of water are 273.15 K and 373.15 K, respectively. The Kelvin scale is

defined by absolute zero and the triple point of water, where ice, liquid water, and water vapor coexist. Absolute zero is 0 K and the triple point of water is defined as 273.16 K.

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## Thermal Expansion

Thermal expansion is the change

in size of a system as its

temperature changes, caused by increased spacing between the atoms or molecules in a substance as it is heated up. The length 𝐿𝐿 of an object changes with a change in temperature ∆𝑇𝑇 proportionally to its original length, 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝛼𝛼𝐿𝐿, where 𝛼𝛼 is the coefficient of

linear expansion. Since 𝛼𝛼 is

typically small, we use the linear approximation, ∆𝐿𝐿 = 𝛼𝛼𝐿𝐿∆𝑇𝑇.

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### Thermal Expansion in Two and Three Dimensions

An object will expand in all dimensions as its temperature changes. In two dimensions, the change in area ∆𝐴𝐴 of an object is ∆𝐴𝐴 = 2𝛼𝛼𝐴𝐴∆𝑇𝑇, where ∆𝑇𝑇 is the change in temperature and 𝐴𝐴 is the original area. In three dimensions, the change in volume is given by 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝛽𝛽𝛽𝛽, where 𝛽𝛽 is the coefficient of volume expansion. As with linear expansion, we can approximate the change in volume by ∆𝛽𝛽 = 𝛽𝛽𝛽𝛽∆𝑇𝑇.

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## Thermal Stress

Changing the temperature of an object while preventing a change in its size creates stress inside the material, known as thermal stress. This stress can sometimes be large enough to cause damage to the object. The stress due to thermal expansion can be found by calculating the change in length due to the change in temperature if the object were not constrained, then calculating the stress induced by compressing the object back to its

constrained size.

For linear expansion, an object with fixed length 𝐿𝐿 that is heated to

produce a change in temperature ∆𝑇𝑇 experiences a stress proportional to its Young’s modulus 𝑌𝑌 and coefficient of linear expansion, 𝐹𝐹𝐴𝐴 = 𝑌𝑌𝛼𝛼∆𝑇𝑇.

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## Internal Energy and Heat

Heat is energy transfer caused by a

temperature difference. The internal energy of an object is the sum of the mechanical energies of its molecules. Heat flow into an object increases the energies of its molecules, increasing the internal energy of the object.

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## Units of Heat

The SI unit of heat is the joule, 𝐽𝐽, like all forms of energy. Heat is also often reported in calories, the temperature needed to heat 1 g of water by 1℃, or the kilocalorie, which is equal to 1000 calories.

The energy contained in food, though often called just calories, is actually kilocalories.

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## Mechanical Equivalent of Heat

Because work can also be done to change the temperature of a

substance, the mechanical equivalent

of heat is defined as the work needed

to produce the same effects as heat transfer. State variables are quantities that depend only on the current state of the system. Because either heat or work can be done to change a system to a particular state, we know that heat and work are not state variables.

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### Temperature Change and Heat Capacity

If a substance does not change phase (for example, from liquid water to ice), the heat added to the system 𝑄𝑄 is given by 𝑄𝑄 = 𝑚𝑚𝑚𝑚∆𝑇𝑇, where 𝑚𝑚 is the substance’s mass, ∆𝑇𝑇 is change in temperature, and 𝑚𝑚 is the specific

heat of the substance. The specific heat is defined by rearranging this

equation and taking the limit of a very small increase in temperature, resulting in the relation 𝑚𝑚 = 𝑚𝑚1 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑.

A container that prevents heat flow is called a calorimeter, and the use of a calorimeter for measurements is called calorimetry. In calorimetry, no heat is transferred from outside the calorimeter, so the heat transferred from a warmer object is equal to the heat transferred into a colder object,

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## Phase Diagrams

A phase diagram shows the pressures and temperatures at which each

phase is stable. Boundaries show

where each phase change occurs. The

critical point is where the gas and

liquid phase can no longer be

distinguished, characterized by the

critical temperature and critical

pressure. The triple point is where all

three phases coexist, and below the triple point, a solid may sublimate, changing directly into a vapor.

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## Equilibrium

When the gas phase of a substance exists below its boiling temperature, it is called a vapor. Liquid in a closed container evaporates until the gas reaches a pressure called the vapor

pressure, where the gas and liquid

are in equilibrium. Adding heat causes the amount of gas to

increase and the amount of liquid to decrease. Equilibrium is also

achieved at the melting and boiling points.

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## Phase Changes

When a substance undergoes a phase change, heat must be added or removed to convert between phases while

temperature remains constant. Adding energy does work to separate tightly bonded

molecules, changing the

substance into a more loosely bonded phase. Removing

energy has the opposite effect.

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## Latent Heat

The heat 𝑄𝑄 is proportional to the mass of the substance 𝑚𝑚 as

𝑄𝑄 = 𝑚𝑚𝐿𝐿, where 𝐿𝐿 is called a latent heat coefficient. There is one latent heat coefficient for each phase change.

For melting and freezing, the relation is 𝑄𝑄 = 𝑚𝑚𝐿𝐿f, where 𝐿𝐿f is the

heat of fusion. For vaporization and condensation, the relation is

𝑄𝑄 = 𝑚𝑚𝐿𝐿v, where 𝐿𝐿v is the heat of vaporization. For sublimation, the relation is 𝑄𝑄 = 𝑚𝑚𝐿𝐿s, where 𝐿𝐿s is the heat of sublimation.

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## Conduction

Conduction is heat transfer through stationary matter by physical

contact. Collisions between lower energy and higher energy molecules directly transfer kinetic energy from the hotter to the colder substance. The rate of conductive heat transfer, 𝑃𝑃, through a material is given by 𝑃𝑃 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = −𝑘𝑘𝐴𝐴 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑, where 𝐴𝐴 is the area of the material, and 𝑘𝑘 is the thermal conductivity.

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## Convection

Convection is heat transfer by the

movement of a fluid. Forced convection is where fans or

pumps are used to move a fluid to transfer heat. Natural convection is driven by the rising of hot fluids and sinking of cold fluids. The

convection rate is approximately proportional to the temperature difference between two objects.

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Radiation is heat transfer by light. The emissivity 𝑒𝑒 of an object describes how

effectively it radiates and absorbs light. The Stefan-Boltzmann law of radiation gives the rate of radiation heat transfer,

𝑃𝑃 = 𝜎𝜎𝐴𝐴𝑒𝑒𝑇𝑇4, where 𝜎𝜎 is a constant, 𝐴𝐴 is the surface area of the object, and 𝑇𝑇 is the temperature in kelvins. The net rate

of heat transfer by radiation between

objects at temperatures 𝑇𝑇1 and 𝑇𝑇2 is 𝑃𝑃 = 𝜎𝜎𝐴𝐴𝑒𝑒(𝑇𝑇24 − 𝑇𝑇14).

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## How to Study this Module

• Read the syllabus or schedule of assignments regularly.

• Understand key terms; look up and define all unfamiliar words and terms.

• As appropriate, work all questions and/or problems assigned and as many additional questions and/or problems as possible.

• Discuss topics with classmates.