The First Law of Thermodynamics: The Law of Conservation of Energy

The statement that "heat and work are mutually convertible" refers to the First Law of Thermodynamics. This fundamental principle in thermodynamics is also known as the Law of Conservation of Energy. It states that energy cannot be created or destroyed, but it can be converted from one form to another.

Conversion of Heat and Work

The First Law of Thermodynamics establishes a relationship between heat and work. It states that any change in the internal energy of a system is equal to the heat added to the system minus the work done by the system. Mathematically, it can be represented as:

ΔU = Q - W

Where:
- ΔU represents the change in internal energy of the system
- Q represents the heat added to the system
- W represents the work done by the system

Interchangeability of Heat and Work

According to the First Law of Thermodynamics, heat and work can be converted from one form to another. This means that under certain conditions, some of the energy supplied to a system as heat can be converted into work, and vice versa.

For example, consider an engine. The engine takes in heat from a high-temperature source, converts a portion of it into useful work, and rejects the remaining heat to a low-temperature sink. This process demonstrates the conversion of heat into work. On the other hand, a heat pump extracts heat from a low-temperature source and supplies it to a high-temperature sink, which demonstrates the conversion of work into heat.

Implications and Applications

The interchangeability of heat and work has significant implications in various fields and applications, including:

1. Thermal power plants: In power generation, heat energy obtained from the combustion of fuel is converted into mechanical work, which is then used to generate electricity.

2. Heat engines: Engines like internal combustion engines and steam turbines convert heat energy into mechanical work, enabling the operation of vehicles and machinery.

3. Refrigeration and air conditioning: Heat pumps and refrigeration systems use work input to transfer heat from a low-temperature region to a high-temperature region, cooling the desired space.

4. Energy conservation: The First Law of Thermodynamics emphasizes the importance of energy conservation and highlights the need for efficient energy utilization in various processes.

In conclusion, the statement that "heat and work are mutually convertible" refers to the First Law of Thermodynamics. This principle establishes the relationship between heat, work, and the change in internal energy of a system. It highlights the interchangeability of heat and work, allowing for various energy conversion processes and applications in different fields.