Learning Outcomes

Upon completing this lesson, you will be able to:

• Distinguish between the Celsius, Fahrenheit, and Kelvin temperature scales, and convert between them.
• State the zeroth law of thermodynamics and explain its role in temperature measurement.
• Calculate the linear and volumetric expansion of materials due to changes in temperature.
• State Gay-Lussac's, Charles's, and Boyle's laws and relate them to absolute temperature.
• Apply the ideal gas law to solve for pressure, volume, temperature, or number of moles in a gas system.

Topics Covered

• Temperature, Thermometers, and Thermodynamics
• Thermal Expansion
• The Gas Law and Absolute Temperature
• The Ideal Gas Law

I. Temperature and Thermometers

A. Temperature

Temperature is a measure of how hot or cold something is. A hot oven is said to have a high temperature, whereas the ice of a frozen lake is said to have a low temperature.

Most materials expand when their temperature is increased. An iron beam is longer when hot than when cold. Concrete roads and sidewalks expand and contract slightly according to temperature, which is why compressible spacers or expansion joints are placed at regular intervals.

The electrical resistance of matter changes with temperature. So too does the color radiated by objects, at least at high temperatures: you may have noticed that the heating element of an electric stove glows with a red color when hot

B. Temperature Scales

Thermometers are instruments designed to measure temperature. In order to do this, they take advantage of some property of matter that changes with temperature. Temperature is generally measured using either the Fahrenheit or the Celsius scale.

$$ T(°C)=\frac{5}{9}[T(°F)-32] \\\text{} \\ T(°F)=\frac{9}{5}T(°C)+32 $$

• The freezing point of water is: $0°$C, or $32°$F.
• The boiling point of water is $100°$C, or $212°$F.

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Example 1

Normal body temperature is $98.6°$F. What is this on the Celsius scale?

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C. Thermal Equilibrium

Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.

For example, you leave a fever thermometer in your mouth until it comes into thermal equilibrium with that environment, and then you read it. Two objects are defined to be in thermal equilibrium if, when placed in thermal contact, no net energy flows from one to the other, and their temperatures don’t change.

The zeroth law of thermodynamics says that if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other.

II. Thermal Expansion

Most substances expand when heated and contract when cooled. However, the amount of expansion or contraction varies, depending on the material.

A. Linear Expansion

Linear expansion occurs when an object is heated.

The change in length $\Delta l$ of almost all solids is, to a good approximation, directly proportional to the change in temperature $\Delta T$ as long as $\Delta T$ is not too large. The change in length is also proportional to the original length of the object, $\Delta l_0$.