Work, Heat, Energy, and the First Law (simplified)

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Note: This is a simplified version, for a version including derivatives go HERE.


Work, W 
Force acting through a distance

In most applications of thermodynamics we are mainly interested in mechanical work due to pressure of a fluid. Then the work is

[math]W=-P\Delta V=-P(V_2-V_1)[/math]

where P is the pressure and V is the volume. The symbol Δ means change - in this case change in volume. The reason for the minus sign is explained below.


Capacity to do work
Internal Energy, U 
The total energy of the system[1]


Energy transferred due to a temperature difference
No heat transfer between a system and its surroundings
Exothermic process 
A process which releases heat
Endothermic process 
A process which adsorbs heat

Heat is denoted by the symbol, Q


Heat and work are considered positive if they are transferred from surroundings to the system.


The laws of thermodynamics are based on observations of the natural world. The first law is based on two observations concerning energy:

  1. Energy can be transferred between a system and its surroundings by only two ways: work and heat
  2. The total energy of a system and its surroundings is always constant (The conservation of energy)

First Law

These two observations can be combined into the First Law of Thermodynamics:

The internal energy of a system is constant unless changed by doing work or by heating


Often in thermodynamics we use a quantity known as the Enthalpy, H. It is defined as: [math]H=U+PV[/math]

Enthalpy is probably the most common thermodynamic quantity used, especially in chemistry and engineering. Especially common is the use of the "enthalpy of reaction". Often this is called just the "heat of reaction"[2]. There are likewise heats of solution, mixing, vaporization, etc.

Heat Capacity

Heat Capacity 
The change in heat per unit temperature

We usually use two specific types of heat capacity:

  • Heat Capacity at constant pressure, CP.
  • Heat Capacity at constant volume, CV.


  1. Note that some references say the internal energy is the energy due to the internal vibrations, etc. In other words that other than kinetic or potential energy. However, the definition used here is equivalent and is easier to understand.
  2. it is actually the heat change at constant pressure. See here for details