Internal Energy of A Closed Thermodynamic System
This above summation of all components of change in internal energy assume that a positive energy denotes heat added to the system or work done on the system, while a negative energy denotes work of the system on the environment.
Typically this relationship is expressed in infinitesimal terms using the differentials of each term. Only the internal energy is an exact differential. For a system undergoing only thermodynamics processes, i.e. a closed system that can exchange only heat and work, the change in the internal energy is
which constitutes the first law of thermodynamics. It may be expressed in terms of other thermodynamic parameters. Each term is composed of an intensive variable (a generalized force) and its conjugate infinitesimal extensive variable (a generalized displacement).
For example, for a non-viscous fluid, the mechanical work done on the system may be related to the pressure p and volume V. The pressure is the intensive generalized force, while the volume is the extensive generalized displacement:
- .
This defines the direction of work, W, to be energy flow from the working system to the surroundings, indicated by a negative term. Taking the direction of heat transfer Q to be into the working fluid and assuming a reversible process, the heat is
- .
- is temperature
- is entropy
and the change in internal energy becomes
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