Temperature Scales

Temperature is a measure related to the average kinetic energy of the particles in a substance.

All matter is made of particles that are constantly moving. When particles have greater average kinetic energy, the temperature is higher. When they have less average kinetic energy, the temperature is lower.

Scientists and everyday users measure temperature using several different scales. The three most common are:

• Celsius (°C)
• Kelvin (K)
• Fahrenheit (°F)

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Temperature and Particle Motion

Particles in matter possess kinetic energy because they are moving.

Temperature is related to the average kinetic energy of these particles.

In general:

Higher temperature → Greater average kinetic energy

Lower temperature → Lower average kinetic energy

For example, particles in hot water have greater average kinetic energy than particles in cold water.

It is important to use the word average. Not every particle in a substance is moving at exactly the same speed.

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Temperature Is Not Heat

Temperature and heat are related, but they are not the same thing.

Temperature

A measure related to the average kinetic energy of particles.

Heat

Energy transferred from a higher-temperature object or region to a lower-temperature one because of a temperature difference.

For example, when a hot metal spoon is placed in cool water:

Hot spoon → Energy transfer → Cooler water

Energy moves from the hotter object to the cooler surroundings until they approach the same temperature.

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Measuring Temperature

A thermometer is used to measure temperature.

Different thermometers may use:

• expanding liquids
• electrical resistance
• thermocouples
• infrared radiation
• digital temperature sensors

Regardless of the method used, the measurement must be expressed using a temperature scale.

The most important temperature scales are Celsius, Kelvin, and Fahrenheit.

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The Celsius Scale

The Celsius scale is widely used for:

• weather
• cooking
• room temperature
• refrigerators
• everyday measurements
• many laboratory measurements

Its symbol is: ^oC

At standard atmospheric pressure, two familiar reference temperatures are approximately:

Water freezes: 0^oC

Water boils: 100^oC

$100^\circ\text{C}$

Some familiar temperatures are:

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The Kelvin Scale

The Kelvin scale is the standard temperature scale used extensively in science.

Its unit is the kelvin, with the symbol: K

Notice that we do not write a degree symbol.

Correct: 300 K

Incorrect: 300^oK

The Kelvin scale is particularly useful because it begins at the lowest possible thermodynamic temperature:

absolute zero.

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Absolute Zero

Absolute zero is: 0 K

which is exactly: -273.15^oC

It represents the theoretical lower limit of thermodynamic temperature.

At absolute zero, a system has the minimum possible thermal energy. In the simple particle model used in introductory science, particle thermal motion is described as reaching its minimum.

A more advanced understanding from quantum mechanics shows that particles do not literally become completely motionless.

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Why Can't Temperature Go Below Absolute Zero?

The Kelvin scale is an absolute temperature scale.

For ordinary thermodynamic systems: T ≥ 0 K

You cannot simply keep removing thermal energy until a conventional temperature of -10 K is reached.

Absolute zero represents the lower limit of the thermodynamic temperature scale.

This makes Kelvin particularly useful in scientific calculations.

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Celsius and Kelvin

Celsius and Kelvin use the same size temperature interval.

A change of: 1^oC

is the same size temperature change as: 1 K

The difference is where the scales begin.

Celsius uses: 0^oC

as the freezing point of water under standard reference conditions.

Kelvin uses: 0 K

as absolute zero.

Therefore: 0^oC = 273.15 K

and: 100^oC = 373.15 K

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Converting Celsius to Kelvin

The conversion is: T_K = T_C + 273.15

For many introductory problems, this may be approximated as:

T_K = T_C + 273

Example

Convert: 25^oC to kelvin.

T_K = 25 + 273.15

T_K = 298.15

Often this would be rounded to: 298 K

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Converting Kelvin to Celsius

To convert in the opposite direction: T_C = T_K - 273.15

Example

Convert: 310 K to Celsius.

T_C = 310 - 273.15

T_C = 36.85

Approximately: 37^oC

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Worked Example: A Cold Temperature

Convert: -20^oC to kelvin.

Use: T_K = T_C + 273.15

Substitute:

T_K = -20 + 273.15

T_K = 253.15 K

Notice that a negative Celsius temperature can still correspond to a positive Kelvin temperature.

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Worked Example: Absolute Zero

Convert: 0 K to Celsius.

T_C = 0 - 273.15

T_C = - 273.15

This is absolute zero.

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Comparing Celsius and Kelvin

The relationship between the two scales is linear.

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The Fahrenheit Scale

The Fahrenheit scale is another temperature scale.

Its symbol is: ^oF

It is used mainly for everyday temperature measurements in the United States and a few other contexts.

At standard atmospheric pressure:

Water freezes at: 32^oF

Water boils at: 212^oF

A typical comfortable indoor temperature might be around:

68^oF to 77^oF

which corresponds approximately to:

20^oC to 25^oC

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Comparing All Three Scales

Important reference points can be compared directly.

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Why Does Science Use Kelvin?

Kelvin is particularly important in physics and chemistry because it is an absolute scale.

Many scientific equations require absolute temperature.

For example, relationships involving:

• gases
• thermodynamics
• thermal radiation
• molecular motion

often use temperature measured in kelvin.

Using Celsius in these equations could produce incorrect results because 0^oC does not represent zero thermal energy.

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Choosing the Appropriate Scale

Different temperature scales are useful in different situations.

Everyday Weather

Usually: ^oC in most countries.

Example:

Today's temperature is 31^oC

Cooking

Usually: ^oC or ^oF

 depending on the country and recipe.

Scientific Calculations

Often: K particularly when using equations involving absolute temperature.

Laboratory Measurements

Celsius may be used for direct measurements, while values are often converted to Kelvin when required for calculations.

Everyday Measurements in the United States

Fahrenheit is commonly used for:

• weather
• ovens
• body temperature
• household temperature settings

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Temperature Differences

Because Celsius and Kelvin intervals are the same size:

A temperature increase from: 20^oC → 30^oC is an increase of: 10^oC

In Kelvin: 293.15 → 303.15 K

This is an increase of: 10 K

Therefore: ΔT = 10^oC = 10 K for a temperature difference.

This does not mean that 10^oC = 10 K as absolute temperatures. It means their interval sizes are equal.

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Temperature and States of Matter

Temperature affects the motion and behaviour of particles.

As a substance is heated, particles generally gain kinetic energy.

This can eventually contribute to changes of state such as:

Solid → Liquid → Gas

During cooling:

Gas → Liquid → Solid

However, during a phase change such as melting or boiling, energy can be transferred without immediately increasing temperature because energy is involved in changing the arrangement and interactions between particles.

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Worked Example: Choosing a Scale

Consider each situation.

Recording Outdoor Temperature

Best choice: ^oC for everyday use in most countries.

Calculating Gas Behaviour

Best choice: K because gas equations generally require absolute temperature.

Following an American Cooking Recipe

Likely choice: ^oF because many American recipes specify oven temperatures in Fahrenheit.

Measuring Laboratory Temperature

A scientist might initially record: 25^oC but convert this to: 298 K if the temperature is needed in a scientific equation.

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Common Misconceptions

Kelvin does not use the degree symbol.

Correct: 300 K

Not: 300^oK

Zero Celsius is not absolute zero.

0^oC = 273.15 K

Absolute zero is: 0 K = -273.15^oC

Temperature and heat are not the same thing.

Temperature is related to average particle kinetic energy, while heat refers to energy transfer caused by a temperature difference.

Particles are not necessarily completely motionless at absolute zero.

The simple particle model may suggest this, but quantum mechanics predicts residual motion associated with the lowest-energy state.

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Did You Know?

Scientists have cooled matter to temperatures extremely close to absolute zero.

At these temperatures, matter can display unusual quantum behaviour that is not normally visible at everyday temperatures.

However, reaching exactly: 0 K

is not achievable by a finite sequence of ordinary cooling processes.

Absolute zero therefore represents a fundamental boundary in thermodynamics.

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Key Terms

Temperature – A measure related to the average kinetic energy of particles.

Kinetic energy – Energy an object or particle has because of its motion.

Celsius (°C) – A commonly used temperature scale with water freezing at approximately ^oC and boiling at 100^oC at standard atmospheric pressure.

Kelvin (K) – The SI unit of thermodynamic temperature and an absolute temperature scale.

Fahrenheit (°F) – A temperature scale commonly used for everyday purposes in the United States.

Absolute zero – The lowest thermodynamic temperature, equal to 0K or -273.15^oC.

Heat – Energy transferred because of a temperature difference.

Thermometer – An instrument used to measure temperature.

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Key Takeaways

• Temperature is related to the average kinetic energy of particles.
• Higher temperature generally means particles have greater average kinetic energy.
• The three commonly encountered temperature scales are Celsius, Kelvin, and Fahrenheit.
• Celsius is widely used for everyday temperatures and laboratory measurements.
• Fahrenheit is commonly used for everyday temperatures in the United States.
• Kelvin is especially important for scientific calculations.
• Kelvin is an absolute temperature scale.
• Absolute zero is: 0 K = -273.15^oC
• Celsius and Kelvin have equal-sized intervals.
• Convert Celsius to Kelvin using: T_K = T_C + 273.15
• Convert Kelvin to Celsius using: T_C = T_K - 273.15
• Kelvin temperatures are written without a degree symbol.
• The appropriate temperature scale depends on the context and application.
• Temperature and heat are related concepts, but they are not the same thing.
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