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This also means the constraint forces do not add to the instantaneous power.) The time integral of this scalar equation yields work from the instantaneous power, and kinetic energy from the scalar product of acceleration with velocity. The fact that the work–energy principle eliminates the constraint forces underlies Lagrangian mechanics. [28]
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: P = d W d t = F ⋅ v {\displaystyle P={\frac {dW}{dt}}=\mathbf {F ...
Every conservative force has a potential energy. By following two principles one can consistently assign a non-relative value to U: Wherever the force is zero, its potential energy is defined to be zero as well. Whenever the force does work, potential energy is lost.
Thermodynamic work is one of the principal kinds of process by which a thermodynamic system can interact with and transfer energy to its surroundings. This results in externally measurable macroscopic forces on the system's surroundings, which can cause mechanical work, to lift a weight, for example, [1] or cause changes in electromagnetic, [2] [3] [4] or gravitational [5] variables.
By the principle of minimum energy, there are a number of other state functions which may be defined which have the dimensions of energy and which are minimized according to the second law under certain conditions other than constant entropy. These are called thermodynamic potentials. For each such potential, the relevant fundamental equation ...
Gibbs free energy is a thermodynamic state function that measures the energy available for a system to do work, and is given by the formula G = H – TS, where H is enthalpy, T is temperature, and S is entropy.
Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work can be dissipated into heat. [ 135 ] [ 136 ] With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian ...
A unit of electrical energy, particularly for utility bills, is the kilowatt-hour (kWh); [3] one kilowatt-hour is equivalent to 3.6 megajoules. Electricity usage is often given in units of kilowatt-hours per year or other periods. [4] This is a measurement of average power consumption, meaning the average rate at which energy is transferred ...