# Introduction to the First Law of Thermodynamics

The First Law of Thermodynamics is the fundamental law of energy conservation for a closed system. It states that the total amount of energy in a closed system is constant, and that energy can neither be created nor destroyed, but only transformed from one form to another. This law is essential to the study of thermodynamics, as it helps to understand and quantify the behavior of energy in various systems.

The First Law of Thermodynamics is a statement of energy conservation in a closed system. For example, in a closed system, the energy that is added to the system must be accounted for, either as work done on the system or as an increase in the internal energy of the system, or both. Conversely, the energy that is removed from the system must also be accounted for, either as work done by the system or as a decrease in the internal energy of the system, or both.

In the context of the First Law of Thermodynamics, work is defined as the transfer of energy due to a force acting through a distance, while heat is the transfer of energy due to a temperature difference. Both work and heat are forms of energy transfer, and they can be quantified in terms of the units of energy, such as joules or calories. Now that we have an understanding of the First Law of Thermodynamics, let’s look at some examples.

# Example 1: Heat and Work in a Piston-Cylinder System

Consider a piston-cylinder system containing a gas that is initially at a pressure of P1 and a volume of V1. The system is isothermally compressed to a final volume of V2. According to the First Law of Thermodynamics, the change in the internal energy of the system is equal to the work done on the system plus the heat added to the system.

In this case, the internal energy of the gas remains constant, since the process is isothermal. Therefore, the change in the internal energy is zero. The work done on the system is given by the area under the curve on a P-V diagram. The heat added to the system is equal to the work done on the system, since the internal energy remains constant. Therefore, the total energy of the system is conserved, in accordance with the First Law of Thermodynamics.

# Example 2: Conservation of Energy in a Chemical Reaction

Chemical reactions involve the transformation of energy from one form to another. According to the First Law of Thermodynamics, the total amount of energy in a system is conserved, and this is true for chemical reactions as well.

For example, the combustion of methane can be represented by the equation: CH4 + 2 O2 -> CO2 + 2 H2O. In this reaction, the reactants (methane and oxygen) have a certain amount of energy, while the products (carbon dioxide and water) have a different amount of energy. The energy difference between the reactants and the products is released as heat, which can be used to do work or to transfer energy to another system.

The First Law of Thermodynamics ensures that the total amount of energy in the system is conserved, regardless of how it is transformed or transferred. This means that the energy released in a chemical reaction must be accounted for, either as work done by the system, heat transferred to the surroundings, or an increase in the internal energy of the system.

# Example 3: Energy Transfer in an Electrical Circuit

Electrical circuits involve the transfer of energy from a power source to a load, such as a light bulb or a motor. According to the First Law of Thermodynamics, the total amount of energy in the system is conserved, and this is true for electrical circuits as well.

For example, consider a simple circuit consisting of a battery, a resistor, and a switch. When the switch is closed, the battery supplies a certain amount of energy to the circuit, which is then dissipated as heat in the resistor. The heat generated in the resistor is equal to the power dissipated, which is given by the product of the voltage across the resistor and the current flowing through it.

The First Law of Thermodynamics ensures that the total amount of energy in the system is conserved, regardless of how it is transformed or transferred. This means that the energy supplied by the battery must be accounted for, either as work done by the circuit, heat dissipated in the resistor, or an increase in the internal energy of the circuit.

In conclusion, the First Law of Thermodynamics is a fundamental law of energy conservation for closed systems. It states that the total amount of energy in a closed system is constant, and that energy can neither be created nor destroyed, but only transformed from one form to another. The examples we have examined demonstrate how the First Law of Thermodynamics applies to various systems, including piston-cylinder systems, chemical reactions, and electrical circuits.