First Law of Thermodynamics

The First Law of Thermodynamics is the law of conservation of energy applied to a thermodynamic system.

The energy stored by a thermodynamic system is called its internal energy U.

The internal energy of a closed system can change if it exchanges work or heat with its surroundings. Therefore, the first law of thermodynamics for a closed system reads as follows:

Where Q is the heat exchanged by the system and Wext is the work done by the surroundings on the system. This is the expression of the first law of Thermodynamics using the IUPAC convention.

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An alternative way of stating the first law is to express it in terms of the work done by the system on its surroundings. It has the same absolute value as the work done by the surroundings on the system but with an opposite sign.

By substituting it in the expression of the first law we obtain:

Where W is the work done by the system on its surroundings. In these pages we will use this expression of the first law, using the so-called Clausius convention.

In these pages the thermodynamic system will be a gas enclosed in a container.

Sign convention:

  • The work done by a gas on its surroundings is positive when it expands. When the gas compresses, the work done is negative.
  • The heat absorbed by a system is positive. The heat discharged by a system to its surroundings is negative.

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The differential form of the first law of Thermodynamics is given by:

The differential symbol used to describe the work and heat in this expression indicates that these two measures are inexact differentials: they depend on the process undergone by the system. The internal energy is it an exact differential: it is a state function whose variation only depends on the initial and final states of the system and not on the process it undergoes.

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