# The First Law of Thermodynamics

## Introduction

In the late 18th century Benjamin Thompson (Count Rumford) asserted that heat was not a fluid known as caloric stored within materials but was associated with motion in some way. This was deduced from seeing that apparently limitless amounts of heat were generated when boring a cannon, especially as the drill became blunter. However, as this predates a good knowledge of atoms and molecules it is unclear what is moving. In the early 19th century James Joule performed quantitative measurements to compare the amount of mechanical work and heat that would raise the temperature of a known quantity of water by the same amount. This is the basis of the First Law of Thermodynamics.

## The System and Surroundings

Before we can start with the first law, it is a good idea to be clear on two important in thermodynamics: the system and the surroundings. The system is the region of the universe under study while the surroundings include everything else in the universe except the system

Figure 1. The system and surroundings

## The First Law of Thermodynamics

Everything that exists, is some form of energy, although there are many different types. Whatever energy is, we cannot create it or destroy it; it can change into different forms, but if we the sum of all the forms of energy, it cannot change. This is a very powerful concept and where the types of energy do not add up, we look for new forms of energy rather than abandon the concept.

In the early versions of the quantum theory, conservation of energy and momentum did not seem to both hold simultaneously. This process of Compton Scattering, where light scatters off an electron and changes energy and momentum. The answer was that light behaves as like particles with a mass which depends on the wavelength. The second example was the used of the conservation of energy to postulate the neutrino by Pauli. In 1956, it was discovered by Frederick Reines et al.

In the 20th century when the advent of quantum theory and the discovery of new particles made even top scientists question the validity of the law at a level of atoms and below. A second example comes later in the century. In beta decay the beta particle can carry off a variable amount of energy and some appears to be lost. Again scientists were willing to conclude that energy is not conserved at a microscopic level. However, the discovery of the neutrino restored the energy balance.

Energy is also used to mean the potential to do work; the greater the ability of something to change the things around it, the more energy it has. Mathematically, the first law is expressed:

ðU=dQ+ðW.

Where dQ is the change in the quantity of heat added to the system, ðU is the change in the internal energy and ðW is the work done on or by the system. The ð sign is used to indicate inexact differentials, meaning that the values of ðU and ðW depend on the path taken.

The sign convention here is that if dU is positive the amount of internal energy increases. This means that dQ stands for the heat energy put into the system and dW for the work done on the system. This is known as the ‘physicists’ convention’.

### Work

 ðW>0 Work is done on the system by the surroundings ðW<0 Work is done by the system on the surroundings

### Heat

 ðQ>0 Heat is added to the system from the surroundings ðQ<0 Heat is released by the system to the surroundings