Temperature Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Temperature.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

A measure of the average kinetic energy of the particles in a substance, determining how hot or cold it is.

How 'hot' or 'cold' something is—how fast its molecules are moving on average.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Temperature starts by identifying what is warmer, what is cooler, and what energy or state variable changes.

Common stuck point: Students often know a formula related to temperature but skip the recognition step: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I tracking thermal energy transfer, particle motion, temperature change, or pressure-volume-temperature relationships?

Worked Examples

Example 1

easy

Convert

37°\text{C}

(human body temperature) to Fahrenheit and Kelvin.

Answer

37 ° C = 98.6 ° F = 310.15 K

First step

Celsius to Fahrenheit:

T_F = \frac{9}{5}T_C + 32 = \frac{9}{5}(37) + 32 = 66.6 + 32 = 98.6°\text{F}

Full solution

2
Celsius to Kelvin: $T_K = T_C + 273.15 = 37 + 273.15 = 310.15 \text{ K}$ .
3
Human body temperature is $98.6°\text{F}$ or $310.15 \text{ K}$ .

Temperature measures the average kinetic energy of particles in a substance. The Kelvin scale starts at absolute zero, where particles have minimum possible energy. Conversion between scales is straightforward.

Example 2

medium

At what temperature do the Celsius and Fahrenheit scales read the same value?

Example 3

medium

Convert

77°\text{F}

to Celsius and to kelvin.

Example 4

hard

At what kelvin temperature is the Celsius reading numerically half of the kelvin reading?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

Liquid nitrogen boils at

77 \text{ K}

. What is this temperature in Celsius and Fahrenheit?

Example 2

hard

Two objects are at

200 \text{ K}

and

400 \text{ K}

. One student says the hotter object is 'twice as hot.' Is this correct? Explain using the concept of absolute temperature and average kinetic energy.

Example 3

easy

Convert 25°C to kelvin.

Example 4

easy

Convert 300 K to Celsius.

Example 5

easy

What does temperature measure about the particles in a substance?

Example 6

easy

A gas at 200 K is heated to 400 K. By what factor does the average particle KE increase?

Example 7

easy

Which is colder: 250 K or -10°C?

Example 8

easy

Is a temperature change of 20°C the same as a change of 20 K?

Example 9

easy

What is the kelvin value of absolute zero?

Example 10

easy

Two gases have the same temperature. What is equal about their particles?

Example 11

medium

A thermometer reads 98.6°F. Convert to Celsius. (

T_C = \frac{5}{9}(T_F - 32)

)

Example 12

medium

At what temperature do Celsius and Fahrenheit read the same value?

Example 13

medium

A gas at 27°C is heated so its average particle KE triples. Find the new temperature in Celsius.

Example 14

medium

Convert -40°C to kelvin and to Fahrenheit. (

T_F = \frac{9}{5}T_C + 32

)

Example 15

medium

Room temperature is about 20°C. Express this in kelvin and explain why scientists prefer kelvin.

Example 16

medium

A gas doubles its absolute temperature from 150 K. Its average particle KE was

E

. What is the new average KE?

Example 17

medium

Why can a small spark at 1000°C cause less burning than a large pot of water at 60°C if you touch it?

Example 18

challenge

A gas sample's average particle speed increases by 50%. By what factor does its absolute temperature change?

Example 19

challenge

If a gas at -23°C is heated until its average particle KE quadruples, find the final Celsius temperature.

Example 20

challenge

Two equal masses of the same gas, A at 300 K and B at 600 K, are mixed in an insulated container. Find the final temperature.

Example 21

medium

Convert 350 K to Celsius and to Fahrenheit. (

T_F = \frac{9}{5}T_C + 32

)

Example 22

medium

A gas cools so its average particle KE halves, starting at 600 K. Find the new absolute temperature.

Example 23

easy

Convert

0°\text{C}

to kelvin.

Example 24

easy

Convert

100°\text{C}

(boiling water) to Fahrenheit. Use

T_F = \tfrac{9}{5}T_C + 32

Example 25

easy

Express

32°\text{F}

in Celsius. Use

T_C = \tfrac{5}{9}(T_F - 32)

Example 26

easy

A bath cools from

40°\text{C}

30°\text{C}

. State the temperature change in kelvin.

Example 27

medium

A gas at

300 \text{ K}

has its absolute temperature increased by a factor of

1.5

. Find the new temperature in

°\text{C}

Example 28

medium

Identify the temperature scale on which a body that has

5\times

the temperature of another has

5\times

the average kinetic energy of its particles.

Example 29

medium

Liquid helium boils at

4.2 \text{ K}

. Convert to Celsius.

Example 30

medium

A weather station logs morning

5°\text{C}

, afternoon

23°\text{C}

. Find the temperature increase in kelvin and Fahrenheit. (

\Delta T_F = (9/5)\Delta T_C

)

Example 31

medium

Two equal masses of the same gas at

200 \text{ K}

and

500 \text{ K}

are mixed in an insulated container. Find the final temperature.

Example 32

medium

A gas is at

-23°\text{C}

. Find the kelvin temperature and the factor by which the absolute temperature must change to reach

477°\text{C}

Example 33

medium

Convert

500°\text{F}

to Celsius (one decimal) and to kelvin (one decimal).

Example 34

medium

A gas in a rigid container at

300 \text{ K}

and

1 \text{ atm}

is heated until pressure doubles. Assuming ideal gas (V constant), find the new temperature.

Example 35

medium

A thermometer is dipped in ice water then in steam at 1 atm. State the two readings in kelvin.

Example 36

hard

A sample's average particle speed doubles. By what factor does the absolute temperature change? Recall

\text{KE} \propto v^2 \propto T

Example 37

hard

A linear thermometer is calibrated so that ice water reads

0

and boiling water reads

80

. What does it read at

25°\text{C}

Example 38

hard

An ideal gas in a sealed flexible container has its kelvin temperature increased from

250 \text{ K}

750 \text{ K}

at constant pressure. By what factor does its volume change?

Example 39

hard

On a thermometer scale called Rankine,

0

Rankine =

0 \text{ K}

and the size of one degree equals one Fahrenheit degree. Find

300 \text{ K}

in Rankine.

Example 40

hard

1 \text{ kg}

of water at

400 \text{ K}

is mixed with

3 \text{ kg}

of water at

300 \text{ K}

(same

c

, no losses). Find the final temperature.

Example 41

challenge

A constant-volume gas thermometer reads

1.20 \text{ atm}

at the freezing point of water and

1.64 \text{ atm}

at the boiling point. Estimate absolute zero in Celsius using a linear extrapolation.

Example 42

challenge

Two identical ideal-gas samples are at

200 \text{ K}

and

800 \text{ K}

. Compare the average particle speeds (ratio of

v

in the hotter to

v

in the cooler).

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Related Concepts

Thermal Energy Heat Transfer