Open a kitchen drawer on a winter morning and pick up a steel spoon and a wooden spoon. The steel spoon feels cold and the wooden one feels almost warm. Both have lain in the same drawer all night. Put a thermometer against each spoon in turn. It shows the same number for both.
Hot, cold and what the hand feels
The hand is a poor judge of hot and cold. It does not sense the state of the spoon. It senses how fast energy leaves the skin. Steel carries energy away from a warm finger quickly, and wood carries it away slowly. So the steel spoon feels colder, although both spoons are in the same state.
We need a quantity that does not depend on the hand. Take a hot block of copper and press it against an equal cold block. Nothing is added from outside. The hot block cools and the cold block warms. After a while both stop changing, and nothing more happens however long we wait.
The final state in Fig 1.1 has a name. Two bodies in contact are in thermal equilibrium when no net energy flows between them. The property that has become equal is the temperature. Energy flows by itself only from the body at the higher temperature to the body at the lower temperature. The flow stops when the temperatures are equal, not when the bodies hold equal energy.
Temperature is the property that decides the direction of energy flow between two bodies in contact. Energy flows from the higher temperature to the lower. Two bodies at the same temperature are in thermal equilibrium and exchange no net energy.
Two spoons and a thermometer
A thermometer is a third body. It is placed against the first spoon and left until its reading stops changing. Then the thermometer and the spoon are in thermal equilibrium. The same is done with the second spoon. If the reading is the same, can we say that the two spoons are in thermal equilibrium with each other? Experience says yes, and the statement is a law of nature.
If bodies A and B are each in thermal equilibrium with a body C, then A and B are in thermal equilibrium with each other.
The zeroth law of thermodynamics sounds obvious, but it is what makes a thermometer honest. Without it, two spoons with the same reading might still exchange energy when touched. The law was named in the 1930s, after the first and second laws had already been numbered. It was more basic than both, so it was called the zeroth.
So the two spoons in the drawer are at the same temperature. The steel spoon only takes energy from your finger faster.
A steel spoon and a wooden spoon have lain in the same drawer all night. The steel spoon feels colder to the touch. Which statement is correct?
A thermometer placed in a jug of water reads \(30\,°\text{C}\). The same thermometer placed in a bucket of water also reads \(30\,°\text{C}\). The water of the jug is poured into the bucket. What happens?
Heat is energy on its way
The energy that flowed from the hot block to the cold block is called heat. Heat is energy that flows from one body to another because of a difference in temperature. Heat is measured in joules, like every other energy. The word describes energy in transit, as work does in Mechanics.
Heat is the energy transferred from one body to another because of a difference in their temperatures. It flows by itself from the higher temperature to the lower.
A body does not contain heat, just as it does not contain work. What a body contains is the energy of its molecules: the kinetic energy of their jiggling and the potential energy of their bonds. This store is the internal energy of the body. Heat that flows in raises the internal energy, and heat that flows out lowers it.
Temperature and internal energy are different things. A bucket of water at \(30\,°\text{C}\) holds far more internal energy than a cup at \(30\,°\text{C}\). Yet no heat flows between them, because their temperatures are equal. On the scale of molecules, a higher temperature means faster random motion; the chapter on kinetic theory makes this exact.
Do not say "this body has more heat". Say "this body is at a higher temperature" or "this body has more internal energy". Heat is always a transfer, like a payment, never a balance.
Which statements are correct?
Putting numbers on temperature
To give temperature a number, we need a property that changes steadily as a body warms. The length of a mercury column in a thin glass tube is one such property. Mercury expands on warming and rises in the tube. But a tube with no marks tells us only that one bath is warmer than another.
Marks come from fixed points, states that always occur at the same temperature. The first is the ice point, pure ice melting under a pressure of one atmosphere. The second is the steam point, pure water boiling under one atmosphere. On the Celsius scale the ice point is called \(0\,°\text{C}\) and the steam point \(100\,°\text{C}\). The gap between them is divided into 100 equal degrees.
The straight line between two points
Let the column be \(l_0\) long at the ice point and \(l_{100}\) long at the steam point. Equal degrees mean that the column grows by equal amounts for equal rises in temperature. So the reading \(l\) is a straight-line function of the temperature \(t\). The fraction of the way from the ice point to the steam point is the same for the column and for the temperature.
The mercury column of a thermometer is \(3.0\,\text{cm}\) long in melting ice and \(23.0\,\text{cm}\) long in steam at one atmosphere. In a bath the column is \(12.0\,\text{cm}\) long. Find the temperature of the bath. How long is the column at \(80\,°\text{C}\)?
The length is the property: \(l_0 = 3.0\,\text{cm}\), \(l_{100} = 23.0\,\text{cm}\). The column grows \(20.0\,\text{cm}\) over 100 degrees.
\(t = \dfrac{l - l_0}{l_{100} - l_0} \times 100\).
\(t = \dfrac{12.0 - 3.0}{20.0} \times 100 = 45\,°\text{C}\). At \(80\,°\text{C}\), \(l = 3.0 + 0.80 \times 20.0 = 19.0\,\text{cm}\).
The bath is at \(45\,°\text{C}\), and at \(80\,°\text{C}\) the column is \(19.0\,\text{cm}\) long.
A mercury column is \(4.0\,\text{cm}\) long in melting ice and \(24.0\,\text{cm}\) long in steam. In warm water it is \(9.0\,\text{cm}\) long. What is the temperature of the water, in °C?
Why must the ice point and the steam point be taken at a pressure of one atmosphere?
In 1742 the Swedish astronomer Anders Celsius described a mercury thermometer with two fixed points and 100 steps between them. He tested with care that melting snow gave the same mark in every weather. In his scale the boiling point of water was 0 and the freezing point was 100. Soon after his death in 1744, the scale was turned the other way up. Warmer then meant a larger number, as it does on every thermometer today.
A doctor places a thermometer under a patient's tongue and waits for a minute or more. The thermometer starts at room temperature. Heat flows into it from the mouth until the two are in thermal equilibrium. Only then does the reading stop rising, and only then is it the temperature of the body. A reading taken too early is always too low.
- Saying that a body "contains heat".A body contains internal energy. Heat is energy in transit, flowing because of a temperature difference.
- Judging temperature by touch.The hand feels how fast energy leaves the skin. Two bodies at one temperature can feel very different.
- Thinking heat flows from the body with more energy to the one with less.Heat flows from the higher temperature to the lower, whatever the amounts of energy stored.
- Measuring the column from the bulb instead of from its ice-point length.Use \(t = 100\,(X - X_0)/(X_{100} - X_0)\): the reading is the fraction of the way from the ice point.