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Secondary 2 · Science II (Physics)
Energy · Heat

Temperature scales

In Mexico the weather forecast gives the temperature in degrees Celsius. If your cousin in Houston sends you a photo of his thermometer, you will see very different numbers. In a physics lab, they would use kelvins. It is the same quantity (how hot or cold something is) measured with three different rulers. How do you convert from one to another without making a mistake?

The three temperature scales

You put a thermometer into a glass of water with crushed ice and it reads $0$. A US thermometer would read $32$ and a laboratory thermometer, $273$. How can the same phenomenon be measured with three such different numbers?

Comparison of the freezing and boiling points of water on the Celsius, Kelvin, and Fahrenheit scales: 0 and 100 °C, 273 and 373 K, 32 and 212 °F. Boiling of water Freezing of water °C 100 0 K 373 273 °F 212 32 All three mark the same phenomena with different numbers
Practice★☆☆
In Mexico, the weather forecast gives the temperature in degrees Celsius, but a friend from the United States gives it to you in degrees Fahrenheit. What is a…

In Mexico, the weather forecast gives the temperature in degrees Celsius, but a friend from the United States gives it to you in degrees Fahrenheit. What is a temperature scale? Name the three scales you know and write the unit symbol for each.

Solve
Practice★☆☆
What is the International System unit for temperature, used in science? And which one do we use in daily life in Mexico? Give an example of each.

What is the International System unit for temperature, used in science? And which one do we use in daily life in Mexico? Give an example of each.

Solve

From Celsius to Kelvin

Comparison between the Celsius and Kelvin scales: the same degree size, with zero shifted by 273 units. °CK 0 °C 273 K 100 °C 373 K +100 +273 at every point: the jump between them (100 degrees) is the same on both scales
Practice★☆☆
On a spring day in Guadalajara, the thermometer reads $25\ ^\circ\text{C}$. Express this temperature in kelvins, remembering that $T_K = t_C + 273$.

On a spring day in Guadalajara, the thermometer reads $25\ ^\circ\text{C}$. Express this temperature in kelvins, remembering that $T_K = t_C + 273$.

Solve
Practice★☆☆
At what temperature, in degrees Celsius, does water freeze? And at what temperature does it boil at sea level? Express both values in kelvins as well.

At what temperature, in degrees Celsius, does water freeze? And at what temperature does it boil at sea level? Express both values in kelvins as well.

Solve
Practice★★☆
During a heatwave in Córdoba, temperatures reach $44\ ^\circ\text{C}$. a) Express this temperature in kelvins. b) How many kelvins difference is there compared to normal…

During a heatwave in Córdoba, temperatures reach $44\ ^\circ\text{C}$.

  1. a) Express this temperature in kelvins.
  2. b) How many kelvins difference is there compared to normal body temperature, $37\ ^\circ\text{C}$?
Solve

Degrees Fahrenheit

A recipe for cookies from the United States says: "preheat the oven to $350\ ^\circ\text{F}$." If you set your stove to $350\ ^\circ\text{C}$, you will burn them. How many degrees Celsius is that temperature?

Two thermometers, one Celsius and one Fahrenheit. The freezing point of water is at 0 °C and 32 °F, and the boiling point at 100 °C and 212 °F. Between the fixed points there are 100 Celsius degrees and 180 Fahrenheit degrees. Also, 20 °C equals 68 °F. Celsius (°C) Fahrenheit (°F) 0 50 100 32 122 212 boiling point of water freezing point of water 20 °C = 68 °F 100 degrees 180 degrees between the fixed points: 100 °C equal 180 °F → 180/100 = 1.8

Back to the beginning: for the recipe, $350\ ^\circ\text{F}$ gives $(350-32)/1.8 \approx 177\ ^\circ\text{C}$. Nothing like $350\ ^\circ\text{C}$.

Practice★☆☆
The classroom temperature is $20\ ^\circ\text{C}$. Calculate what this is in degrees Fahrenheit using the expression $T_F = 1.8 \times t_C + 32$.

The classroom temperature is $20\ ^\circ\text{C}$. Calculate what this is in degrees Fahrenheit using the expression $T_F = 1.8 \times t_C + 32$.

Solve
Practice★★☆
A kitchen thermometer bought in the United States reads $122\ ^\circ\text{F}$. Calculate the temperature in degrees Celsius by rearranging the expression…

A kitchen thermometer bought in the United States reads $122\ ^\circ\text{F}$. Calculate the temperature in degrees Celsius by rearranging the expression $T_F = 1.8 \times t_C + 32$.

Solve
Practice★★☆
An American biscuit recipe says to bake at $392\ ^\circ\text{F}$. a) Convert this temperature to degrees Celsius. b) Then express it in kelvins.

An American biscuit recipe says to bake at $392\ ^\circ\text{F}$.

  1. a) Convert this temperature to degrees Celsius.
  2. b) Then express it in kelvins.
Solve

When do Celsius and Fahrenheit read the same?

A Celsius thermometer and a Fahrenheit thermometer show different numbers almost all the time. But is there some temperature at which both show the same number? To find out, we use the same letter $t$ for the value on both scales and solve an equation with the unknown on both sides.

It is the only temperature at which they coincide: below it, the Fahrenheit number is smaller; above it, it is larger.

Practice★★★
There is a temperature at which a Celsius thermometer and a Fahrenheit thermometer show the same number. The figure shows both scales side by side: a) Set up the…

There is a temperature at which a Celsius thermometer and a Fahrenheit thermometer show the same number. The figure shows both scales side by side:

Comparison between the Celsius and Fahrenheit temperature scales °C 100 80 60 40 20 0 −20 ? °F 212 150 100 50 32 0 ? t = ?
  1. a) Set up the equation $t = 1.8 \times t + 32$ and solve it.
  2. b) At what temperature does this coincidence occur?
  3. c) Check your result by applying the conversion formula to the obtained value.
Solve

Absolute zero

Thermometer with Kelvin and Celsius scales: 373 K is 100 °C, 273 K is 0 °C, and absolute zero, 0 K or −273 °C, is the lower limit. 373 K · 100 °C 273 K · 0 °C 0 K · −273 °C boiling point of water freezing point of water absolute zero: lower limit in kelvins there are never negative values
Practice★☆☆
Zero on the Kelvin scale is called absolute zero. How many degrees Celsius does it correspond to? Why do you think it is called this?

Zero on the Kelvin scale is called absolute zero. How many degrees Celsius does it correspond to? Why do you think it is called this?

Solve
Practice★★★
In Yakutsk (Siberia), temperatures as low as $-50\ ^\circ\text{C}$ have been measured. Look at the thermometer scale in the diagram: a) Express this temperature in…

In Yakutsk (Siberia), temperatures as low as $-50\ ^\circ\text{C}$ have been measured. Look at the thermometer scale in the diagram:

°C 100 50 0 −50 −100 −150 −200 −250 −50 °C Yakutsk 0 K = −273 °C absolute zero −300 °C ?
  1. a) Express this temperature in kelvins.
  2. b) Could a temperature of $-300\ ^\circ\text{C}$ ever be measured anywhere in the universe? Justify your answer using the concept of absolute zero.
  3. c) Can there be negative temperatures on the Celsius scale? And on the Kelvin scale? Give reasons for both answers.
Solve

Comparing and ordering temperatures

Two glasses of water, one at 300 K and the other at 30 °C, next to a thermometer with kelvin and Celsius scales: 30 °C matches 303 K, above 300 K. 300 K 30 °C K °C 303 300 30 27 30 °C = 303 K > 300 K
Practice★★☆
Which is hotter: a glass of water at $300\ \text{K}$ or a glass of water at $30\ ^\circ\text{C}$? Convert both values to the same scale before comparing.

Which is hotter: a glass of water at $300\ \text{K}$ or a glass of water at $30\ ^\circ\text{C}$? Convert both values to the same scale before comparing.

Solve
Practice★★☆
Order the following temperatures from lowest to highest, first expressing them all in degrees Celsius: a) $50\ ^\circ\text{F}$ b) $280\ \text{K}$ c) $0\ ^\circ\text{C}$

Order the following temperatures from lowest to highest, first expressing them all in degrees Celsius:

  1. a) $50\ ^\circ\text{F}$
  2. b) $280\ \text{K}$
  3. c) $0\ ^\circ\text{C}$
Solve
Practice★★★
We want to know what a temperature increase of $10\ ^\circ\text{C}$ is equivalent to on the other scales. a) Express $20\ ^\circ\text{C}$ and $30\ ^\circ\text{C}$ in…

We want to know what a temperature increase of $10\ ^\circ\text{C}$ is equivalent to on the other scales.

  1. a) Express $20\ ^\circ\text{C}$ and $30\ ^\circ\text{C}$ in kelvins and in degrees Fahrenheit.
  2. b) Calculate the difference between both values on each of the three scales.
  3. c) Conclude which two scales have degrees of the same size and which scale has the smallest degrees.
Solve

Summary

Let's practice! 8 medium exercises in this section
★★☆ A kitchen thermometer bought in the United States reads $122\ ^\circ\text{F}$. Calculate…★★☆ On a trip to Miami, Yasmin feels unwell and the chemist's thermometer reads…★★☆ Which is hotter: a glass of water at $300\ \text{K}$ or a glass of water at…
Let's practice! 8 hard exercises in this section
★★★ There is a temperature at which a Celsius thermometer and a Fahrenheit thermometer show…★★★ Liquid nitrogen, widely used in laboratories and modernist cuisine, boils at…
See all the exercises in this section