Temperature Conversions Chemistry Tutorial

Key Concepts

• Temperature is a measure of the average kinetic energy of the particles in an object.

  Adding energy, for example, heat, to an object increases the kinetic energy of the particles which is observed as an increase in temperature.
  When an object loses energy, kinetic energy of the particles decreases and is observed as a decrease in temperature.

• Several temperature scales are in common use:

  ⚛ Kelvin Scale based on the kelvin unit (K) is the SI unit of temperature. ⁽¹⁾

  ⚛ Celsius Scale based on degrees Celsius (°C), closely related to the Centigrade scale.⁽²⁾

  ⚛ Fahrenheit Scale based on degrees Fahrenheit (°F), commonly used in North America.

• Kelvin Scale is based on the following fixed points:

  ⚛ The zero point is absolute zero, the lowest temperature theoretically obtainable.

  ⚛ The temperature at which solid, liquid and gaseous water can coexist indefinitely (the triple-point temperature of water) is assigned a value of 273.16 K

• Celsius Scale is based on:

  ⚛ a triple-point temperature of water of 0.01°C at 1 atm pressure

  ⚛ freezing point of water as 0.00°C at 1 atm pressure

  ⚛ boiling point of water as 100.00°C at 1 atm pressure

  A dfference in temperature of 1°C = a difference of 1K

• Fahrenheit Scale is based on:

  ⚛ freezing point of water of 32°F

  ⚛ boiling point of 212°F

  A dfference in temperature of 1°F = a difference of ⁵/₉°C = a difference of ⁵/₉K

• To convert a temperature in Celsius (°C) to a temperature in Kelvin (K)

  Kelvin (K) = °C + 273.15

• To convert a temperature in Kelvin (K) to a temperature in Celsius (°C)

  °C = K − 273.15

• To convert a temperature in Fahrenheit (°F) to a temperature in Celsius (°C)

  °C = ⁵/₉ × (°F − 32)

• To convert a temperature in Celsius (°C) to a temperature in Fahrenheit (°F)

  °F = (⁹/₅ × °C) + 32

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Temperature Conversions: Kelvin, Celsius, Fahrenheit

Let's compare three common temperature scales: Kelvin, Celsius and Fahrenheit:

The divisions in the Celsius scale and the Kelvin scale are the same size:

For example, the difference between the temperature at which water boils and freezes at 1 atm:

In °C: 100°C − 0°C = 100°C

In K: 373.15 K − 273.15 K = 100 K

A difference of 1°C is the same as a difference of 1K, the only difference is the starting point (at 1 atm, the freezing point of water is 0°C or 273.15 K).
This makes converting between temperatures in °C and K straight-forward.

If you have a temperature in °C we can just add 273.15 to arrive at a temperature in Kelvin (K):

T (K) = T (°C) + 273.15

To convert 25°C to a temperature in Kelvin (K):

T (K) = T (°C) + 273.15 = 25 + 273.15 = 298.15 K

If we have a temperature in Kelvin (K) we can just subtract 273.15 to arrive at a temperature in °C

T (°C) = T (K) − 273.15

To convert 0 K to a temperature in Celsius (°C):

T (°C) = T (K) − 273.15 = 0 − 273.15 = −273.15 (°C)

If you need to convert a temperature in Fahrenheit to a temperature in °C or K, it is a little bit trickier because not only is the starting point different (freezing point of water) but also the size of the divisions are also different, so that a difference of 1°F is NOT the same size as a difference of 1°C.

A difference of 10°C = 10 K = 18°F

A difference of 1°C = 1 K = 1.8°F

Or, we can put this another way:

A difference of 1.8°F = 1°C = 1 K

A difference of (1.8°F ÷ 1.8) = (1°C ÷ 1.8) = (1 K ÷ 1.8)

A difference of 1°F ≈ 0.55555555°C ≈ 0.55555555 K

The "5"s after the decimal point will just keep on repeating forever, so this is not a satisfactory way of converting Fahrenheit to Celsius or Kelvin!
So we express the value as a fraction:

1.8 = ⁹/₅

So, a difference of 1.8°F = ⁹/₅°F = 1°C = 1 K

And, a difference of 1°F = ⁵/₉°C = ⁵/₉ K

So if we are given a temperature in Fahrenheit and we need to convert it to Celsius, first we need to subtract 32 from the temperature in °F (that is, the freezing point of water) and then multiply this by ⁵/₉

T (°C) = (T (°F) − 32) × ⁵/₉

To convert 68°F to Celcius:

T (°C) = (T (°F) − 32) × ⁵/₉ = (68 − 32) × ⁵/₉ = 36 × ⁵/₉ = 20°C

If we need to convert a temperature in °C to a temperature in °F; first we multiply the temperature in °C by ⁹/₅ and then we add 32 (freezing point of water):

T (°F) = [⁹/₅ × T (°C)] + 32

To convert 25°C to Fahrenheit:

T (°F) = [⁹/₅ × T (°C)] + 32 = [⁹/₅ × 25 °C)] + 32 = [45] + 32 = 77°F

To summarise:

• Converting Celsius (°C) to Kelvin (K)

  Kelvin (K) = °C + 273.15

• Converting Kelvin (K) to Celsius (°C)

  °C = K − 273.15

• Converting Fahrenheit (°F) to Celsius (°C)

  °C = ⁵/₉ × (°F − 32)

• Converting Celsius (°C) to Fahrenheit (°F)

  °F = (⁹/₅ × °C) + 32

Worked Examples of Temperature Conversions: Celsius and Kelvin

Question 1: Convert 30°C to a temperature in Kelvin (K)

Solution:

Kelvin (K) = °C + 273.15 = 30 + 273.15 = 303.15 K

Question 2: Convert −15°C to a temperature in Kelvin (K)

Solution:

Kelvin (K) = °C + 273.15 = −15 + 273.15 = 258.15 K

Question 3: Convert 300 K to a temperature in Celsius (°C)

Solution:

°C = K − 273.15 = 300 - 273.15 = 26.85°C

Question 4: Convert 25 K to a temperature in Celsius (°C)

Solution:

°C = K − 273.15 = 25 - 273.15 = −248.15°C

Worked Examples of Temperature Conversions: Fahrenheit, Celsius and Kelvin

Question 1: Convert 30°C to a temperature in Fahrenheit (°F)

Solution:

°F = (⁹/₅ × °C) + 32 = (⁹/₅ × 30) + 32 = 54 + 32 = 86°F

Question 2: Convert 300 K to a temperature in Fahrenheit (°F)

Solution:

Convert K to °C

°C = K − 273.15 = 300 - 273.15 = 26.85°C

Convert °C to °F

°F = (⁹/₅ × °C) + 32 = (⁹/₅ × 26.85) + 32 = 48.33 + 32 = 80.33°F

Question 3: Convert 60°F to a temperature in Celsius (°C)

Solution:

°C = ⁵/₉ × (°F − 32) = ⁵/₉ × (60 − 32) = ⁵/₉ × (28) = 15.56°C

Question 4: Convert −20°F to a temperature in Kelvin (K)

Solution:

Convert temperature in °F to temperature in °C:

°C = ⁵/₉ × (°F − 32) = ⁵/₉ × (−20 − 32) = ⁵/₉ × (−52) = −28.89°C

Convert temperature in °C to temperature in K:

Kelvin (K) = °C + 273.15 = −28.89 + 273.15 = 244.26 K