Temperature, heat and the measurement of temperature

Heat and temperature

Touch a metal rail and a wooden bench on a cold morning: the metal feels colder, though both are at the same temperature. Your hand is feeling the flow of heat, not the temperature.

• Heat is energy that flows from a hotter body to a colder one because of their difference in temperature. It is measured in joules.
• Temperature tells which way heat will flow. Two bodies in contact stop exchanging heat when they reach the same temperature: they are in thermal equilibrium.

A thermometer works because it comes into equilibrium with what it touches.

Scales of temperature

A thermometer uses a property that changes steadily with temperature: the length of a mercury column, the pressure of a gas, the resistance of a wire. Two fixed points set the scale: the ice point and the steam point at one atmosphere.

So $T_F = \tfrac95 T_C + 32$, and the kelvin, the SI unit, has the same size as the Celsius degree: $T = T_C + 273.15$.

You should find that $37\ ^\circ\text{C}$ is $98.6\ ^\circ\text{F}$, and that the two scales agree only at $-40$.

Watch out. A change of $1\ \text{K}$ is the same as a change of $1\ ^\circ\text{C}$. Only the readings differ.

A faulty thermometer

If a thermometer reads $5$ in melting ice and $95$ in steam, its $90$ divisions span $100$ true degrees. A reading of $23$ is $18$ divisions above the ice point, so the true temperature is $\dfrac{18}{90} \times 100 = 20\ ^\circ\text{C}$.

A worked example

A doctor abroad reads a child's temperature as $102.2\ ^\circ\text{F}$. Is that a fever?

1. Celsius. $T_C = \dfrac59(102.2 - 32) = \dfrac59 \times 70.2 = 39.0\ ^\circ\text{C}$.
2. Kelvin. $39.0 + 273.15 = 312.15\ \text{K}$.
3. Verdict. Normal is about $37\ ^\circ\text{C}$, so yes, a fever.

Practise with new numbers

Try it in Python

The program changes some everyday temperatures between the scales and corrects the faulty thermometer.

Remember these

• Heat is energy that flows; temperature decides the direction.
• $T_F = \tfrac95 T_C + 32$; $T = T_C + 273.15$.
• A change of $1\ \text{K}$ equals a change of $1\ ^\circ\text{C}$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Change $-10\ ^\circ\text{C}$ to Fahrenheit and kelvin.

2. Why does metal feel colder than wood at the same temperature?

3. The temperature of a room rises by $15\ ^\circ\text{C}$. By how many kelvin does it rise?

4. Is heat a property of a body, like its mass?