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When an object is immersed in a liquid, the liquid exerts an upward force, which is known as the buoyant force, that is proportional to the weight of the displaced liquid. The sum force acting on the object, then, is equal to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force).
The interpretation of the continuity equation for mass is the following: For a given closed surface in the system, the change, over any time interval, of the mass enclosed by the surface is equal to the mass that traverses the surface during that time interval: positive if the matter goes in and negative if the matter goes out.
Thus water behaves as though it is an ideal gas that is already under about 20,000 atmospheres (2 GPa) pressure, and explains why water is commonly assumed to be incompressible: when the external pressure changes from 1 atmosphere to 2 atmospheres (100 kPa to 200 kPa), the water behaves as an ideal gas would when changing from 20,001 to 20,002 ...
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Expressions as a function of temperature for the two empirical parameters and are given for water, seawater, helium-4, and helium-3 in the entire liquid phase up to the critical temperature . The special case of the supercooled phase of water is discussed in Appendix D of reference. [ 5 ]
For example, in the reaction CH 4 + 2 O 2 → CO 2 + 2 H 2 O, the stoichiometric number of CH 4 is −1, the stoichiometric number of O 2 is −2, for CO 2 it would be +1 and for H 2 O it is +2. In more technically precise terms, the stoichiometric number in a chemical reaction system of the i-th component is defined as
Complex fluids are mixtures that have a coexistence between two phases: solid–liquid (suspensions or solutions of macromolecules such as polymers), solid–gas , liquid–gas or liquid–liquid . They exhibit unusual mechanical responses to applied stress or strain due to the geometrical constraints that the phase coexistence imposes.
The first solution to this problem was provided by Freeman Dyson and Andrew Lenard in 1967–1968, [1] [2] but a shorter and more conceptual proof was found later by Elliott Lieb and Walter Thirring in 1975 using the Lieb–Thirring inequality. [3] The stability of matter is partly due to the uncertainty principle and the Pauli exclusion ...