The only ways the energy of a closed system can be changed are through transfer of energy by work or by heat. Further, based on the experiments of Joule and others, a fundamental aspect of the energy concept is that energy is conserved; we call this the first law of thermodynamics.

These considerations are summarized in words as follows:

change in the amount of energy contained within the system during some time interval = net amount of energy transferred in across the system boundary by heat transfer during the time interval - net amount of energy transferred out across the system boundary by work during the time interval

This word statement is just an accounting balance for energy, an energy balance. It requires that in any process of a closed system the energy of the system increases or decreases by an amount equal to the net amount of energy transferred across its boundary.

The phrase net amount used in the word statement of the energy balance must be carefully interpreted, for there may be heat or work transfers of energy at many different places on the boundary of a system. At some locations the energy transfers may be into the system, whereas at others they are out of the system.

The two terms on the right side account for the net results of all the energy transfers by heat and work, respectively, taking place during the time interval under consideration.

The energy balance can be expressed in symbols as
E2 - E1 = Q - W

which shows that an energy transfer across the system boundary results in a change in one or more of the macroscopic energy forms: kinetic energy, gravitational potential energy, and internal energy. All previous references to energy as a conserved quantity are included as special cases of the equation.

Note that the algebraic signs before the heat and work terms of the equation are different. This follows from the sign conventions previously adopted. A minus sign appears before W because energy transfer by work from the system to the surroundings is taken to be positive.

A plus sign appears before Q because it is regarded to be positive when the heat transfer of energy is into the system from the surroundings.

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