Prove ⅆ𝐻 = [𝑉 + 𝐶𝑉 (𝜕𝑇 ) 𝜕𝑃 ]ⅆ𝑃 +𝐶𝑃(𝜕𝑇 ) ⅆ𝑉
时间: 2024-05-18 08:11:53 浏览: 116
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This equation is an expression of the fundamental thermodynamic relation, which relates changes in the internal energy (dH) of a system to changes in its pressure (dP), volume (dV), and temperature (dT). The equation is a statement of energy conservation, that the total change in the internal energy of a system is equal to the work done on the system plus the heat added to the system.
The left-hand side of the equation, dH, represents the change in the internal energy of the system. The right-hand side of the equation is a sum of two terms. The first term, [V + CV(dT/dP)]dP, represents the work done on the system by a change in pressure, where V is the volume of the system, and CV is the heat capacity at constant volume. The second term, CP(dT/dV)dV, represents the heat added to the system by a change in volume, where CP is the heat capacity at constant pressure.
The equation can be derived from the first and second laws of thermodynamics, and is a fundamental equation in the study of thermodynamics. Its validity has been experimentally verified in a wide range of systems and conditions.
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