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The internal energy is essentially defined by the first law of thermodynamics which states that energy is conserved:
where ΔU is the change in internal energy of a system during a process, Q is heat added to a system, W is the mechanical work done on a system (measured in joules in SI) and W' is energy added by all other processes. Thus, the internal energy of a system is all the energy of the system associated with its microscopic components like atoms and molecules when viewed from a reference frame at rest with respect to the system.
In a mechanical system, the energy is stored in the form of internal energy being transferred either from potential energy or from kinetic energy. For example, when a block slides over a rough surface, the mechanical energy lost due to friction is transformed into internal energy that is stored temporarily inside the block and inside the surface, as evidenced by a measurable increase in the temperature of both block and surface. In submicroscopic scale this internal energy is associated with vibration of atoms about their equilibrium positions. Such internal atomic motion involves both kinetic and potential energy. internal energy is associated with vibration of atoms about their equilibrium positions. Such internal atomic motion involves both kinetic and potential energy.
Frictional Work:
When an object is pushed along a surface, the energy converted to heat/ work is given by:
where Fn is the normal force, μk is the coefficient of kinetic friction, and x is the coordinate along which the object transverses. This work is the work done on a horizontal rough surface.
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