Definition: The first low of thermodynamics is the application of the conservation of energy. Energy is neither be create or not be destroyed. The total amount of energy of the earth is constant. The energy can be transferred from one form to another form.

The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics. The first law gives the relationship between heat transfer, work done, and the change in internal energy of a system.

The 1st law of thermodynamics can be mathematically stated as follows:

 §dQ = §dW

In Thermodynamic Cycle, a cyclic process the systems undergoes, the cyclic integral of heat added is equal to integral of work done. The first law equation can be written in the form,

 §(dQ – dW) = 0

First Law Of Thermodynamics Equation

Equation dU = dQ – dW is a corollary to the first law of thermodynamics. It shows that there exists a property internal energy (U) of the system, such that a change in its value is equal to the difference in heat entering and work leaving the system.

The sign convention for heat and work in the first law of thermodynamics is represented in the picture below.

Summary of Terms for the First Law of Thermodynamics, ΔU=Q−W

Term Definition
UInternal energy—the sum of the kinetic and potential energies of a system’s atoms and molecules. Can be divided into many subcategories, such as thermal and chemical energy. Depends only on the state of a system (such as its P, V, and T), not on how the energy entered the system. Change in internal energy is path independent.
Q Heat—energy transferred because of a temperature difference. Characterized by random molecular motion. Highly dependent on the path. 
 entering a system is positive.
W Work—energy transferred by a force moving through a distance. An organized, orderly process. Path-dependent. 
 done by a system (either against an external force or to increase the volume of the system) is positive.

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