Internal energy change via heat and work

The first law of thermodynamics is a formulation of the law of conservation of energy in the context of thermodynamic processes. It relates the change in internal energe of the system, work done on or by the system and the amount of heat supplied to or withdrawn from the system during a thermodynamic process.

Notation:

  1. \(\delta\) (delta) denotes an inexact, path-dependent differential.

  2. \(d\) denotes an exact, path-independent differential.

Notes:

  1. This formula applies to any infinitesimal thermodynamic process, be in static or not.

  2. This formula can be extended to finite processes by changing infinitesimal changes to finite ones.

  3. The work done by the system onto the environment is positive, and work done onto the system by the environment is negative.

  4. The heat flowing from the environment into the system is positive, and the heat flowing into the environment out of the system is negative.

Links:

  1. Wikipedia.

internal_energy_change

Infinitesimal change in internal energy of the system.

Symbol:

dU

heat_supplied_to_system

Infinitesimal amount of heat supplied to the system during its interaction with the environment.

Symbol:

delta(Q)

Latex:

\(\delta Q\)

work_done_by_system

Infinitesimal work done by the system on its environment.

Symbol:

delta(W)

Latex:

\(\delta W\)

law

dU = delta(Q) - delta(W)

Latex:
\[d U = \delta Q - \delta W\]