First Law of Thermodynamics

The first law of thermodynamics is also known as the law of conservation of energy. It states that energy cannot be created or destroyed; it can only be converted from one form to another. This law is fundamental to the study of thermodynamics and has many applications in engineering.

Heat and Work Conversion

The first law of thermodynamics can be expressed mathematically as follows:

ΔU = Q - W

where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. This equation indicates that energy can be converted from heat to work and vice versa.

When heat is added to a system, the internal energy of the system increases. This energy can be used to do work if the system is allowed to expand or if there is a pressure difference. Conversely, if work is done on a system, its internal energy increases, and this energy can be released as heat if the system is allowed to contract or if there is a pressure difference.

Efficiency of Carnot Engine

The Carnot engine is a theoretical engine that operates between two heat reservoirs and is the most efficient engine possible. It operates on the Carnot cycle, which consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

The efficiency of the Carnot engine is given by:

η = 1 - Tc/Th

where η is the efficiency, Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir. This equation shows that the efficiency of the engine depends only on the temperature difference between the two reservoirs.

Conclusion

The first law of thermodynamics states that energy can be converted from one form to another. Heat and work are mutually convertible, which means that energy can be converted from heat to work and vice versa. The Carnot engine is the most efficient engine possible, and its efficiency depends only on the temperature difference between the hot and cold reservoirs.