﻿ # Laws of Thermodynamics

After this section you should be able to:

• Understand the concepts of heat, temperature and internal energy
• Convert between temperature scales
• Use the First Law of Thermodynamics in calculations involving work and heat associated with biological systems
• Discuss the laws of thermodynamics

Reference

• Introduction to Biological Physics for Health and Life Sciences (2010 or 2018) Sections 17.1–17.2, and 22.1-22.3

## Introduction

We are all intimately familiar with ideas such as heat and temperature in our everyday lives. We use ovens and fires to cook our food, and air conditioners to keep ourselves cool. When we stand outside on a sunny summer's day, it just feels hot. But what are the physical phenomena underlying these concepts? The area of science concerned with describing heat and its relationship with energy is called thermodynamics. Thermodynamics is an extremely powerful field of study that allows us to understand much of the fundamental nature of interactions in the universe. With the ability to explain phenomena as simple as boiling the kettle, to something as complex as the creation of a new star, thermodynamics is an important scientific tool capable of both practical and profound insights into nature.

Thermodynamics elegantly explains complex phenomena using only a small collection of fundamental laws. Einstein himself was entranced by thermodynamics, famously stating

"A law is more impressive the greater the simplicity of its premises, the more different are the kinds of things it relates, and the more extended its range of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown."

With this impressive endorsement, let's take a closer look at the four fundamental laws that underpin all of thermodynamics.

## The Zeroth Law of Thermodynamics

The zeroth law is incredibly important as it allows us to define the concept of a temperature scale.

If two systems are each in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

For example, consider two separate cups of boiling water. If we place a thermometer into the first cup, it gets warmed up by the water until it reads 100°C. We now say that the thermometer is in thermal equilibrium with the first cup of water. Next, we move the thermometer into the second cup of boiling water, and it continues to read 100°C. The thermometer is therefore also in thermal equilibrium with the second cup of water. Using the logic of the zeroth law, we can conclude that the two separate cups of boiling water are in thermal equilibrium with each other. The zeroth law therefore enables us to use thermometers to compare the temperatures of any objects we like.

Why call this the "zeroth" law you may ask? The truth is that the other thermodynamic laws (the first, second, and third) had already been named by the time this one was formulated. However, scientists thought that it was so important that it should go before all the others, and hence it was termed the zeroth law.

## The First Law of Thermodynamics

Examples of thermodynamic systems that we might choose to study are the human body, chemicals in a test tube, or stars. The first law states that every one of these systems has an internal energy (\(U\)), and that the internal energy can be changed in two ways, through work (\(W\)) or by exchange of heat (\(Q\)). In essence, the internal energy is the total sum of all the energy contained within the system. This energy can be in many forms, for example in molecular motion, or stored in chemical bonds. The first law enables us to treat all the energy as a whole, and not worry about these specifics. The formal notation of the first law is:

The change in internal energy of a system (\(\Delta U\)) is due to heat gain or loss (\(Q\)) and work done (\(W\)): \$\$\Delta U = Q - W\$\$

• When the system gains internal energy, \(\Delta U\)) is positive.
• When the system gains heat, \(Q\) is positive.
• \(W\) is positive when work is done by the system

The internal energy of a system changes when work is done on, or by, the system. For example, a human body will do work on the pedals of a bike when riding up a hill (work is done by the body) in turn lowering the internal energy of the body. As another example, we could do work on a glass of juice by stirring it, increasing the internal energy of the juice.

Besides work, the internal energy of a system is changed through the exchange of heat. Heat can be trasferred in many ways. We could surround a system with an environment at a different temperature, for example we raise the internal energy of an ice cream when we carry it around outside on a hot day. As another example, we could place a system in contact with a hot object to increase the system's internal energy, like when we place a saucepan of water on a stove top. There are many ways that we can transfer heat to or from a system, but in the eyes of the first law, they are all equal.

There is a further mechanism that can change the internal energy of a system, particularly relevant when looking at biological applications of thermodynamics. The internal energy of a system can be increased by taking in material such as food. Before digestion, food has a high amount of potential energy stored in its chemical bonds. Through a set of chemical reactions called metabolism, our bodies transform the food into lower energy molecules, extracting the energy released during this process. If we are modelling a human or other animal as a thermodynamic system, we need to include this energy in our calculations. We do this by including a term for metabolism, \(E\), in the First Law of Thermodynamics: \$\$\Delta U = Q - W + E\$\$

Thus the change in internal energy of an animal (\(\Delta U\)) is due to three different quantities: the heat transferred to the body (\(Q\)), the work done by the body (\(W\)), and the energy gained from the ingestion and metabolism of food (\(E\)).

## The Second Law of Thermodynamics

The second law of thermodynamics places an observation of everyday life into a formal statement:

Heat flows spontaneously from a substance at a higher temperature to a substance at a lower temperature and does not flow spontaneously in the other direction.

For instance, consider an ice cube in a hot water bath. You will only ever observe heat flowing spontaneously (i.e. without any work being done) from the hot water bath into the ice cube, eventually melting it. You will never ever see heat flowing from the ice cube to the water, making the ice cube even colder and the water even warmer. Such behaviour as this has never been observed, in any context.

The idea that heat flows from hot to cold, and not from cold to hot, has surprisingly profound effects, and many great thinkers have spent a great deal of time contemplating the phenomenon. The second law also enables us to describe a quantity called entropy, a measure of the disorder of a system. On the grandest scales, entropy is always increasing, allowing us to define such philosophical concepts as time only running in one direction, and even to go so far as predicting the eventual fate of the universe.

## The Third Law of Thermodynamics

The third law introduces the concept of absolute zero, the lowest possible temperature theoretically possible. Absolute zero corresponds to -273.15°C, the point where there is no thermal motion. In preference to the Celsius (°C) scale, we use the SI unit for temperature called the kelvin where \$\$T(^\circ C) = T(K) -273.15\$\$

Absolute zero occurs at 0 K.

Specifically, the third law states that absolute zero can never be attained:

It is not possible to lower the temperature of any system to absolute zero in a finite number of steps.

Although physicists can never cool an object to precisely absolute zero, they do now routinely cool gases to less than a millionth of a degree above absolute zero in order to study the exotic phases of matter that occur at such low temperatures.

## How am I doing?

The temperature at the coldest known place in the universe (the Boomerang Nebula), of 1K, is equivalent to -272°C.

True
False

When two objects are in thermal equilibrium, no net heat flows between them.

True
False

When a body is heated, its internal energy decreases.

True
False

## Summing Up

Before attending the lecture make sure that you:

Understand the idea of thermal equilibrium
Appreciate that the energy internal to a system can be affected by various energy interactions with its environment
Can convert temperatures between units of °C and kelvin