# Thermal Physics

We’re all naturally familiar with the concept of temperature, but how do we actually define a substance’s temperature using physics? Describing the internal thermal energy of a substance using a temperature turns out to be a fundamental aspect of physics and thermodynamics.

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## What is temperature?

The thermal energy of a substance is proportional to the (average) kinetic energy of its constituent molecules or atoms. In a system with two objects, the hotter object has a higher temperature and higher average kinetic energy. Thermal energy flows from the hotter object to the colder one until both objects reach the same temperature. This is formalised in the zeroth law of thermodynamics.

### The zeroth law of thermodynamics

Although the zeroth law of thermodynamics was only the fourth law to be proposed, it was deemed so fundamental to thermal physics that it now comes first.

Figure 1. The zeroth law is a fundamental concept of thermal physics that provides a basis for the definition of temperature and mathematical laws about the effects of temperature. Source: Ross MacDonald, StudySmarter.

The zeroth law states:

If two objects A and C are both independently in thermal equilibrium with some third object B, then A and C are also in equilibrium with each other. This also shows all three objects are of equal temperature.

This (seemingly obvious) law defines temperature as a property that describes the direction of any thermal energy transfer between objects. The zeroth law is important as it shows that the transfer of thermal energy is controlled by physical temperatures rather than an object’s total thermal (kinetic) energy.

### Temperature scales

Having defined what temperature is, we now need a way to measure it. In order to compare the temperatures of different objects, a scale is needed. A temperature scale is defined by two fixed points at specific temperatures, with a number of increments between them.

There are currently three main temperature scales in use around the world:

Celsius

• This temperature scale, proposed by Swedish astronomer Anders Celsius in 1742, is used by most of the world.
• The fixed points used by the Celsius scale are the freezing point (0°C) and the boiling point of water (100°C at atmospheric pressure 1.01⋅105 Pa), with 100 increments of 1°C between them.

Fahrenheit

• The Fahrenheit scale, proposed by German physicist Daniel Fahrenheit in the 18th century, is primarily used in the United States.
• The scale is also based on the freezing (32°F) and boiling (212°F) points of water, with 180 increments between them.

Kelvin (absolute temperature)

• The absolute temperature scale uses the fixed points of the triple point of water (273.16°K) and absolute zero (0°K). These were selected because they do not vary with atmospheric pressure, unlike the Celsius and Fahrenheit scales.
• When defining the Kelvin scale, it was decided that each increment should be equal to 1°C to make comparisons simpler. This is why there are exactly 273.16°F between the two fixed points.
• The kelvin is the SI unit of temperature. To convert between temperatures in Celsius and kelvin, we can use the formula T(K)=T(C)+273.16.
• Temperatures on the kelvin scale are always positive.

The triple point of water (or other substances) is the temperature and pressure at which all three phases of matter (solid, liquid, and gas) can coexist. The different phases also exist in thermal equilibrium, with no net thermal energy transfers between them. For pure water, the triple point is 0.01°C at 611.2 Pa.

## Heat transfer

Now that we have an understanding of what temperature is, we can explore how thermal energy (heat) is transferred between objects in a system. This field of physics is known as thermodynamics, which deals with the relationships between heat, work, temperature, and energy in systems.

### The laws of thermodynamics

We have already encountered the zeroth law of thermodynamics, which provides the basis for the definition of temperature. Let us now explore the remaining laws of thermodynamics.

#### The first law of thermodynamics

Q is used to represent the change in thermal energy in the first law of thermodynamics, which states:

A change in internal energy (ΔU) of a system is comprised of the thermal energy added to the system (Q) plus any net gain or loss of energy via work done to or by the system (W).

$\Delta U = Q -W$

This shows that energy cannot be created or destroyed.

#### The second law of thermodynamics

The second law introduces the property of entropy, represented by S.

When two previously isolated systems are allowed to interact, they will eventually reach a state of thermal equilibrium. The total entropy (S) of the combined system will be greater than the sum of the two isolated systems.

A unit of heat transferred (δQ) is a product of the temperature of the systems (T) and the change in total entropy (∂s).

$\delta Q = T \cdot ∂ S$

#### The third law of thermodynamics

The third law states that, as a system’s temperature approaches absolute zero and all thermal energy is removed, the system reaches a constant ground state. The value of entropy at this point is known as the system residual entropy. If the system only has one possible microstate at absolute zero, then the residual entropy will also be zero. The constant value of a system’s residual entropy at absolute zero increases with the number of possible system microstates.

$S = k_B \cdot \ln(\Omega)$

Here, S is the system residual entropy, kB is the Boltzmann constant, and Ω is the number of microstates.

A pure crystal is an example of a material that would have zero residual entropy, as there is only one valid crystalline structure (microstate) its atoms can adopt.

### Internal energy

All substances (solid, liquid, or gas) have internal energy (U), which is the sum of the kinetic energy and potential energy of its constituent molecules. The levels of kinetic and potential energy each individual molecule has are random (within the range of energy contained in the system), but we can understand these properties of the larger substance by using the average energies of its molecules.

The kinetic energy of molecules in a substance is directly related to its temperature, while their potential energy depends on the phase of the substance. The potential energy is made up of electrostatic potential energy. The attractive forces between molecules are ‘stretched’ as the average distance between molecules increases when transitioning from solid to liquid, or liquid to gas. This increases their electrostatic potential energy, just as increasing the distance between an object and the earth raises its gravitational potential energy.

Figure 2. The diagram shows how the kinetic and electrostatic potential components of a substance’s internal energy increase through phase changes as energy is transferred into the substance at a steady rate. Source: Ross MacDonald, StudySmarter.

The diagram shows how energy is transferred into a substance at a steady rate. During phase changes, the kinetic energy of its molecules (temperature) remains constant, while the electrostatic potential energy increases. This is because, during the phase change, the input energy is transferred to an increase in electrostatic potential as the substance melts or evaporates and forces between the molecules change.

Outside of phase changes, the electrostatic potential remains relatively constant, and all the input energy is converted into molecular kinetic energy, increasing the temperature of the substance. The total internal energy is a sum of these two components and increases at the same rate as energy is transferred into the substance.

• In solids, the electrostatic potential energy is a large negative, as the strong bonds between atoms or molecules require significant energy to be broken.
• In liquids, the electrostatic forces between molecules are smaller, so the potential is a smaller negative, as less energy is required to break them.
• In gases, the electrostatic potential is near zero, as the forces between molecules are very weak or negligible.

#### Latent heat

The contribution of electrostatic potential energy to the total internal energy creates a property known as the specific latent heat of a substance.

Specific latent heat L is defined as the energy required to change a substance’s phase per unit mass while at a constant temperature.

$L = \frac{E}{M}$

Here, E is the energy required for the phase change, while M is the mass of the substance.

#### Specific heat

Different substances require varying amounts of thermal energy transfer to change their temperatures by the same amount. Water is an example of a substance with a high specific heat capacity (think of how long it takes to boil water for a cup of tea). This is because a large amount of energy needs to be transferred into the water by the kettle to raise its temperature to 100°C. An example of a low specific heat capacity is iron, and therefore most steels (think of how quickly a steel spoon heats up in the mug of tea you just made).

The specific heat capacity of a substance is calculated as:

Change in energy = mass · specific heat capacity · change in temperature

$\Delta E = mc \Delta \theta$

Here, ΔE is the change in internal energy, m is the mass of substance, c is the specific heat capacity, and Δθ is the change in heat energy. Specific heat capacity is given in units of J⋅kg-1K-1.

How much energy is required to boil water for a cup of tea? Using a 2000W kettle, how long would this take to boil?

Quantity of water: 0.25kg

Starting temperature: 21°C

Specific heat capacity of water: 4200 J⋅kg-1K-1

Assuming we’re making tea at an altitude near sea level, our target boiling temperature is 100°C. Therefore, the required change in temperature is 79°C.

To determine the change in energy, we now multiply:

$$\Delta E = 0.25 \cdot 79 \cdot 4200 = 82950 J$$

The power rating of an appliance in watts tells us how many joules of energy per second it uses. Modelling the kettle as 100% efficient, we can divide to find the time it took to boil:

$$t = \frac{82950}{2000} = 41.48 s$$

## Ideal gases

We can describe macroscopic properties, such as the mass, temperature, or pressure of gases, relatively easily. However, in order to fully understand how gases behave, we also need to know what’s happening at the level of an individual particle. The number of atoms (or molecules) in a volume of gas is described using a unit called mole, the SI unit for the amount of substance, which indicates the number of atoms or molecules in a given sample of a given substance.

One mole of a substance is a quantity that contains as many elementary entities (atoms or molecules) as there are atoms in 0.012kg of carbon-12. That number of entities is 6.02⋅1023, also known as the Avogadro constant NA.

The Avogadro constant can be used to calculate the number of atoms N in n moles of a substance:

$N = n \cdot N_A$

An ideal gas is a theoretical substance whose molecules occupy negligible space and are not affected by electrostatic force interactions. These properties mean it will obey the ideal gas laws exactly.

## Thermal Physics - Key takeaways

• The zeroth law of thermodynamics states that if two objects A and C are both independently in thermal equilibrium with some third object B, then A and C are also in equilibrium with each other.
• Temperature scales are defined by two fixed points at specific temperatures, with a number of increments between them. The absolute temperature scale uses units of kelvin (°K) that are equal to Celsius (°C), with 0°K at absolute zero (-273.16°C).
• The internal energy of a substance is comprised of molecular kinetic energy and electrostatic potential energy. During phase changes, the temperature and molecular kinetic energy remain constant while electrostatic potential increases. As the temperature of each phase increases, the electrostatic potential remains constant while molecular kinetic energy increases.
• Moles are the SI unit for the amount of substance that indicates the number of atoms or molecules in a given sample of a given substance.
• An ideal gas is an approximation of a real gas with certain assumptions that allow its behaviour to be modelled using the ideal gas equation.

#### Flashcards in Thermal Physics 130

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What is Thermal Physics?

Thermal physics is a subject covering the fields of thermodynamics and the kinetic theory of gases. Statistical mechanics is also used to study these by approximating the behavior of large numbers of particles.

How to calculate thermal energy?

The amount of energy in a substance is its internal energy (U), comprised of thermal energy and electrostatic potential energy. To calculate the amount of thermal energy required for temperature changes the specific heat capacity of materials can be used: Change in energy (E) = mass (m) · specific heat capacity (c) · change in temperature (ΔT).

What is Q in thermal physics?

The term Q represents a change in the thermal energy of a substance. The first law of thermodynamics states: a change in internal energy (ΔU) of a system is comprised of the thermal energy added to the system (Q) plus any net gain or loss of energy via work done to or by the system (W).

## Test your knowledge with multiple choice flashcards

Which of the following is not a method for thermal energy transfer?

What is conductive heat transfer?

Which of the following parameters does not affect the heat transfer coefficient

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