A Text book of Thermodynamics
A Text book of Thermodynamics
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The origin may therefore be chosen anywhere in the plane of zero volume.
If the energy is taken as a function of the volume and entropy, we have : dU=TdS . Pdr .... (2) T- 8U -- aU (3) ~8S' 1 } "fc ' An equation in which the entropy of a homogeneous fluid is expressed as a function of its energy and volume is called by Planck (1909) a canonical equation.
Equations (3) are the conditions of equilibrium.
The condition for stability requires that : SU > TSS - ptv . . (4) in which the variations ar...e to be construed strictly, i. E. , quantities of order higher than the first are not to be neglected. This is equivalent to (2) of 51.
Now if we pass from one point (v, S, U) on the surface to an adjacent point (r + 8r, S + 8S, U + U) we shall have .
+ (6) Thus, from (3), (4) and (5) we have, as the condition for stable equilibrium of a homogeneous phase : VAN DER WAALS' EQUATION 241 the conditions for which inequality are : a 2 u a s u as 2 asar >0 (6). A2u >o (7) a 2 u a 2 u } ' ^ 2 " asar a*- 2 and hence ^-^ > (8) Inequalities (6) and (7) show that the surface is, at every point which corresponds with a homogeneous phase in stable equilibrium, convex downwards in every direction.
What to read after A Text book of Thermodynamics?
You can find similar books in the "Read Also" column, or choose other free books by J R James Riddick Partington to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The origin may therefore be chosen anywhere in the plane of zero volume.
If the energy is taken as a function of the volume and entropy, we have : dU=TdS . Pdr .... (2) T- 8U -- aU (3) ~8S' 1 } "fc ' An equation in which the entropy of a homogeneous fluid is expressed as a function of its energy and volume is called by Planck (1909) a canonical equation.
Equations (3) are the conditions of equilibrium.
The condition for stability requires that : SU > TSS - ptv . . (4) in which the variations ar...e to be construed strictly, i. E. , quantities of order higher than the first are not to be neglected. This is equivalent to (2) of 51.
Now if we pass from one point (v, S, U) on the surface to an adjacent point (r + 8r, S + 8S, U + U) we shall have .
+ (6) Thus, from (3), (4) and (5) we have, as the condition for stable equilibrium of a homogeneous phase : VAN DER WAALS' EQUATION 241 the conditions for which inequality are : a 2 u a s u as 2 asar >0 (6). A2u >o (7) a 2 u a 2 u } ' ^ 2 " asar a*- 2 and hence ^-^ > (8) Inequalities (6) and (7) show that the surface is, at every point which corresponds with a homogeneous phase in stable equilibrium, convex downwards in every direction.
What to read after A Text book of Thermodynamics?
You can find similar books in the "Read Also" column, or choose other free books by J R James Riddick Partington to read onlineMoreLess
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