# 9.1: Heat, Temperature, and Thermal Energy

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

The temperature of basalt lava at Kilauea (Hawaii) reaches 1,160 degrees Celsius (2,120 degrees Fahrenheit). A crude estimation of temperature can be determined by looking at the color of the rock: orange-to-yellow colors are emitted when rocks (or metals) are hotter than about 900 degrees Celsius; dark-to-bright cherry red is characteristic as material cools to 630 degrees Celsius; faint red glow persists down to about 480 degrees Celsius. For comparison, a pizza oven is commonly operated at temperatures ranging from 260 to 315 degrees Celsius.

## Heat, Temperature, and Thermal Energy Transfer

The first theory about how a hot object differs from a cold object was formed in the 18th century. The suggested explanation was that when an object was heated, an invisible fluid called “caloric” was added to the object. Hot objects contained more caloric than cold objects. The caloric theory could explain some observations about heated objects (such as that the fact that objects expanded as they were heated) but could not explain others (such as why your hands got warm when you rub them together).

In the mid-19th century, scientists devised a new theory to explain heat. The new theory was based on the assumption that matter is made up of tiny particles that are always in motion. In a hot object, the particles move faster and therefore have greater kinetic energy. The theory is called the kinetic-molecular theory and is the accepted theory of heat. Just as a baseball has a certain amount of kinetic energy due to its mass and velocity, each molecule has a certain amount of kinetic energy due to its mass and velocity. Adding up the kinetic energy of all the molecules in an object yields the thermal energy of the object.

When a hot object and a cold object touch each other, the molecules of the objects collide along the surface where they touch. When higher kinetic energy molecules collide with lower kinetic energy molecules, kinetic energy is passed from the molecules with more kinetic energy to those with less kinetic energy. In this way, heat always flows from hot to cold and heat will continue to flow until the two objects have the same temperature. The movement of heat from one object to another by molecular collision is called conduction.

Heat is the energy that flows as a result of a difference in temperature. We use the symbol Q for heat. Heat, like all forms of energy, is measured in joules.

The temperature of an object is a measurement of the average kinetic energy of all the molecules of the object. You should note the difference between heat and temperature. Heat is the sum of all the kinetic energies of all the molecules of an object, while temperature is the average kinetic energy of the molecules of an object. If an object was composed of exactly three molecules and the kinetic energies of the three molecules are 50 J, 70 J, and 90 J, the heat would be 210 J and the temperature would be 70 J.

The terms hot and cold refer to temperature. A hot object has greater average kinetic energy but may not have greater total kinetic energy. Suppose you were to compare a milliliter of water near the boiling point with a bathtub full of water at room temperature. The bathtub contains a billion times as many water molecules, and therefore has a higher total kinetic energy and more heat. Nonetheless, we would consider the bathtub colder because its average kinetic energy, or temperature, is lower.

Adjust the temperature slider in the simulation below to visualize its effect on the average kinetic energy of the molecules making up the Golden Gate Bridge:

Interactive Element

## Temperature Scales: Celsius and Kelvin

A thermometer is a device used to measure temperature. It is placed in contact with an object and allowed to reach thermal equilibrium with the object (they will have the same temperature). The operation of a thermometer is based on some property, such as volume, that varies with temperature. The most common thermometers contain liquid mercury, or some other liquid, inside a sealed glass tube. The liquid expands and contracts faster than the glass tube. Therefore, when the temperature of the thermometer increases, the liquid volume expands faster than the glass volume, allowing the liquid to rise in the tube. The positions of the liquid in the tube can then be calibrated for accurate temperature readings. Other properties that change with temperature can also be used to make thermometers; liquid crystal colors and electrical conductivity change with temperature, and are also relatively common thermometers.

The most commonly used temperature scale in the United States is the Fahrenheit scale. However, this scale is rarely used throughout the world; the metric temperature scale is Celsius. This scale, based on the properties of water, was devised by the Swedish physicist, Anders Celsius (1704 – 1744). The freezing point of water is 0°C and the boiling point of water was assigned to be 100°C. The kinetic energies between these two points was divided evenly into 100 “degrees Celsius”.

The Kelvin or “Absolute” temperature scale is the scale often used by chemists and physicists. It is based on the temperature at which all molecular motion ceases; this temperature is called absolute zero and is 0 K. This temperature corresponds to 273.15°C exactly, but we can round to 273°C when performing calculations and conversions. Since absolute zero is the coldest possible temperature, there are no negative values on the Kelvin temperature scale. Conveniently, the Kelvin and Celsius scales have the same definition of a degree, which makes it very easy to convert from one scale to the other. The relationship between Celsius and Kelvin temperature scales is given by:

K = °C + 273

On the Kelvin scale, water freezes at 273 K and boils at 373 K.

Example 9.1.1

Convert 25°C to Kelvin.

Solution

K = °C + 273 = 25°C + 273 = 298 K

Yummy! These cookies look delicious. But watch out! They just finished baking in a hot oven, so the cookie sheet is too hot to handle without an oven mitt. Touching the cookie sheet with bare hands could cause a painful burn. However, the air inside the oven doesn’t hurt. How can this be? Explore the Hot Oven simulation below to find out:

Interactive Element

## Summary

• The thermal energy, or heat, of an object is obtained by adding up the kinetic energy of all the molecules within it.
• Temperature is the average kinetic energy of the molecules.
• Absolute zero is the temperature where molecular motion stops and is the lowest possible temperature.
• Zero on the Celsius scale is the freezing point of water and 100°C is the boiling point of water.
• The relationship between Celsius and Kelvin temperature scales is given by K = °C + 273.

## Review

1. Convert 4.22 K to °C.
2. Convert 37°C to K.
3. If you had beeswax attached to one end of a metal skewer and you placed the other end of the skewer in a flame, what would happen after a few minutes?
4. Which contains more heat, a coffee cup of boiling water or a bathtub of room temperature water?

## Explore More

Use this resource to answer the questions that follow.

1. Which material was a better conductor of heat?
2. Explain why metals feel cold even when they are at room temperature.

## Resources

This MIT video examines the phenomenon of Joule heating through the perspective of a blender, reproducing the experiment of the English physicist James Prescott Joule.