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All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a continuity equation, which states that the change in the quantity in a volume is equal to the total net "flux" of the quantity through the surface of the volume. The following sections discuss continuity equations in ...
For example, the law of conservation of energy states that the energy of a closed system must remain constant. It can neither increase nor decrease without coming in contact with an external system. If we consider the whole universe as a closed system, the total amount of energy always remains the same.
Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law.This is the first of two theorems (see Noether's second theorem) published by mathematician Emmy Noether in 1918. [1]
Continuity equations are a stronger, local form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy in the universe is fixed. This statement does not rule out the possibility that a quantity of energy could disappear ...
The law of conservation of mass can only be formulated in classical mechanics, in which the energy scales associated with an isolated system are much smaller than , where is the mass of a typical object in the system, measured in the frame of reference where the object is at rest, and is the speed of light.
The convective form emphasizes changes to the state in a frame of reference moving with the fluid. The conservation form emphasizes the mathematical interpretation of the equations as conservation equations for a control volume fixed in space (which is useful from a numerical point of view).
Note that the state equation, given by the first law of thermodynamics (i.e. conservation of energy), is written in the following form (assuming no mass transfer or radiation). This form is more general and particularly useful to recognize which property (e.g. c p or ρ {\displaystyle \rho } ) influences which term.
Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas. The initial and final volumes and pressures of the fixed amount of gas, where the initial and final temperatures are the same (heating or cooling will be required to meet this condition), are related ...