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The Clausius–Clapeyron equation [8]: 509 applies to vaporization of liquids where vapor follows ideal gas law using the ideal gas constant and liquid volume is neglected as being much smaller than vapor volume V. It is often used to calculate vapor pressure of a liquid. [9]
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The Antoine equation is a class of semi-empirical correlations describing the relation between vapor pressure and temperature for pure substances. The Antoine equation is derived from the Clausius–Clapeyron relation. The equation was presented in 1888 by the French engineer Louis Charles Antoine (1825–1897). [1]
The Clausius–Clapeyron relation does not make sense for second-order phase transitions, [1] as both specific entropy and specific volume do not change in second-order phase transitions. Quantitative consideration
At the melting pressure, liquid and solid are in equilibrium. The third law demands that the entropies of the solid and liquid are equal at T = 0. As a result, the latent heat of melting is zero, and the slope of the melting curve extrapolates to zero as a result of the Clausius–Clapeyron equation. [13]: 140
In 1842 Clapeyron published his findings on the "optimal position for the piston at which the various valves should be opened or closed." [1] [4] In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot's principle, what is now known as the second law of ...
Thus, we use more complex relations such as Maxwell relations, the Clapeyron equation, and the Mayer relation. Maxwell relations in thermodynamics are critical because they provide a means of simply measuring the change in properties of pressure, temperature, and specific volume, to determine a change in entropy. Entropy cannot be measured ...
A control valve is a valve used to control fluid flow by varying the size of the flow passage as directed by a signal from a controller. [1] This enables the direct control of flow rate and the consequential control of process quantities such as pressure , temperature , and liquid level.