Exercises: Temperature scales

In Spain, 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.

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

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.

Nora's home freezer is at about $255\ \text{K}$. What is this temperature in degrees Celsius?

The classroom temperature is $20\ ^\circ\text{C}$. Calculate what this is in degrees Fahrenheit using the expression $T_F = 1,8 \cdot t_C + 32$.

The normal body temperature of a healthy person is about $37\ ^\circ\text{C}$. Express it in kelvins.

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

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?

A kitchen thermometer bought in the United States reads $122\ ^\circ\text{F}$. Calculate the temperature in degrees Celsius by rearranging the expression $T_F = 1,8 \cdot t_C + 32$.

On a trip to Miami, Yasmin feels unwell and the chemist's thermometer reads $102,2\ ^\circ\text{F}$. Convert the value to degrees Celsius and state whether she has a fever, knowing that a fever is considered to start at $38\ ^\circ\text{C}$.

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.

In a Canadian village, the thermometer reads $-10\ ^\circ\text{C}$. Express this temperature:

1. a) In kelvins.
2. b) In degrees Fahrenheit.

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.

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) $0\ ^\circ\text{C}$

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, $37\ ^\circ\text{C}$?

The Fahrenheit scale sets $32\ ^\circ\text{F}$ at the freezing point of water.

1. a) Using the expression $T_F = 1,8 \cdot t_C + 32$, verify that $0\ ^\circ\text{C}$ is indeed equivalent to $32\ ^\circ\text{F}$.
2. b) Calculate at how many degrees Fahrenheit water boils, that is, what $100\ ^\circ\text{C}$ is equivalent to.

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:

1. a) Set up the equation $t = 1,8 \cdot t + 32$ 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.

Liquid nitrogen, widely used in laboratories and modernist cuisine, boils at $77\ \text{K}$.

1. a) Express this temperature in degrees Celsius.
2. b) Then convert it to degrees Fahrenheit.
3. c) Why must liquid nitrogen be handled using special gloves and safety goggles?

Iker remarks: "Yesterday it was $15\ ^\circ\text{C}$ and today it's $30\ ^\circ\text{C}$, so today it is twice as hot."

1. a) Express both temperatures in kelvins.
2. b) Calculate how much the temperature has increased in kelvins and assess whether it is reasonable to say "twice as hot".
3. c) Explain why comparing temperatures in this way would only make sense, at most, on a scale whose zero is absolute zero.

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.

The Celsius scale fixed its $0$ and $100$ at two specific points for water.

1. a) What are these two points?
2. b) How many degrees are there between these two points on the Celsius scale? And on the Kelvin scale? And on the Fahrenheit scale (between $32\ ^\circ\text{F}$ and $212\ ^\circ\text{F}$)?
3. c) Using these intervals, explain why a Fahrenheit degree is smaller than a Celsius degree.

On the surface of the Moon, the temperature reaches $127\ ^\circ\text{C}$ during the day and drops to $-173\ ^\circ\text{C}$ at night.

1. a) Express both temperatures in kelvins.
2. b) Calculate the temperature variation between day and night, in kelvins and in degrees Celsius.
3. c) Explain why this variation is the same on both scales.

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

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.

Normal body temperature is $37\ ^\circ\text{C}$, and with a high fever it can reach $40\ ^\circ\text{C}$.

1. a) Express both temperatures in kelvins and in degrees Fahrenheit.
2. b) By how much has the temperature risen on each of the three scales?
3. c) Explain why the increase is the same in degrees Celsius and in kelvins, but not in degrees Fahrenheit.