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# 3: The First Law of Thermodynamics

Energy is conserved in all processes, including those associated with thermodynamic systems. The roles of heat transfer and internal energy change vary from process to process and affect how work is done by the system in that process. We will see that the first law of thermodynamics explains that a change in the internal energy of a system comes from changes in heat or work. Understanding the laws that govern thermodynamic processes and the relationship between the system and its surroundings is therefore paramount in gaining scientific knowledge of energy and energy consumption.

• 3.0: Prelude to The First Law of Thermodynamics
In a car engine, heat is produced when the burned fuel is chemically transformed into mostly CO2 and H2O, which are gases at the combustion temperature. These gases exert a force on a piston through a displacement, doing work and converting the piston’s kinetic energy into a variety of other forms—into the car’s kinetic energy; into electrical energy to run the spark plugs, radio, and lights; and back into stored energy in the car’s battery.
• 3.1: Thermodynamic Systems
A thermodynamic system includes anything whose thermodynamic properties are of interest. It is embedded in its surroundings or environment; it can exchange heat with, and do work on, its environment through a boundary, which is the imagined wall that separates the system and the environment. In reality, the immediate surroundings of the system are interacting with it directly and therefore have a much stronger influence on its behavior and properties.
• 3.2: Work, Heat, and Internal Energy
Positive (negative) work is done by a thermodynamic system when it expands (contracts) under an external pressure. Heat is the energy transferred between two objects (or two parts of a system) because of a temperature difference. Internal energy of a thermodynamic system is its total mechanical energy.
• 3.3: First Law of Thermodynamics
Now that we have seen how to calculate internal energy, heat, and work done for a thermodynamic system undergoing change during some process, we can see how these quantities interact to affect the amount of change that can occur. This interaction is given by the first law of thermodynamics, which argues you cannot get more energy out of a system than you put into it. We will see in this chapter how internal energy, heat, and work all play a role in the first law of thermodynamics.
• 3.4: Thermodynamic Processes
The thermal behavior of a system is described in terms of thermodynamic variables. For an ideal gas, these variables are pressure, volume, temperature, and number of molecules or moles of the gas. For systems in thermodynamic equilibrium, the thermodynamic variables are related by an equation of state. A heat reservoir is so large that when it exchanges heat with other systems, its temperature does not change.
• 3.5: Heat Capacities of an Ideal Gas
• 3.6: Adiabatic Processes for an Ideal Gas
When an ideal gas is compressed adiabatically, work is done on it and its temperature increases; in an adiabatic expansion, the gas does work and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment.
• 3.A: The First Law of Thermodynamics (Answer)
• 3.E: The First Law of Thermodynamics (Exercise)
• 3.S: The First Law of Thermodynamics (Summary)

Thumbnail: Different thermodynamic paths taken by a system in going from state A to state B. For all transitions, the change in the internal energy of the system $$ΔE_{int}=Q−W$$ is the same.