Bridgman thermodynamic formulas - Revision history

Carl McBride: /* References */ Added a related paper by Cooper and Russell

2011-10-13T10:02:04Z

References: Added a related paper by Cooper and Russell

← Older revision		Revision as of 12:02, 13 October 2011
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	<references/>		<references/>
	;Related reading		;Related reading
			*[http://arxiv.org/abs/1102.1540 James B. Cooper and T. Russell "On the Mathematics of Thermodynamics", arXiv:1102.1540v1 Tue, 8 Feb (2011)]
	*[http://arxiv.org/abs/1108.4760 James B. Cooper "Thermodynamical identities - a systematic approach", arXiv:1108.4760v1 Wed, 24 Aug (2011)]		*[http://arxiv.org/abs/1108.4760 James B. Cooper "Thermodynamical identities - a systematic approach", arXiv:1108.4760v1 Wed, 24 Aug (2011)]
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

Carl McBride: /* References */ Added a link to the preprint by James Cooper

2011-10-13T09:56:30Z

References: Added a link to the preprint by James Cooper

← Older revision		Revision as of 11:56, 13 October 2011
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://arxiv.org/abs/1108.4760 James B. Cooper "Thermodynamical identities - a systematic approach", arXiv:1108.4760v1 Wed, 24 Aug (2011)]
	[[Category: Classical thermodynamics]]		[[Category: Classical thermodynamics]]

Carl McBride: /* Table II */

2011-10-06T12:12:25Z

Table II

← Older revision		Revision as of 14:12, 6 October 2011
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	====internal energy====		====internal energy====

	:<math> \left. \partial H \right\~~vert_Q~~ = - \left. \partial Q \right\vert_H = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) - p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>		:<math> \left. \partial H \right\vert_U = - \left. \partial U \right\vert_H = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) - p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

	:<math> \left. \partial G \right\~~vert_Q~~ = - \left. \partial Q \right\vert_G = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) +S \left( T\left. \frac{\partial V}{\partial T} \right\vert_p + p\left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>		:<math> \left. \partial G \right\vert_U = - \left. \partial U \right\vert_G = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) +S \left( T\left. \frac{\partial V}{\partial T} \right\vert_p + p\left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>

	:<math> \left. \partial A \right\~~vert_Q~~ = - \left. \partial Q \right\vert_A = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>		:<math> \left. \partial A \right\vert_U = - \left. \partial U \right\vert_A = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			====enthalpy====

			:<math> \left. \partial G \right\vert_H = - \left. \partial H \right\vert_G = -V(C_p+S) + TS \left. \frac{\partial V}{\partial T} \right\vert_p </math>

			:<math> \left. \partial A \right\vert_H = - \left. \partial H \right\vert_A = -\left(S+p \left. \frac{\partial V}{\partial T} \right\vert_p \right) \left(V-T \left. \frac{\partial V}{\partial T} \right\vert_p \right) + p \left. \frac{\partial V}{\partial p} \right\vert_T </math>

	====Gibbs energy function====		====Gibbs energy function====

			:<math> \left. \partial A \right\vert_G = - \left. \partial G \right\vert_A = -S\left(V+p \left. \frac{\partial V}{\partial p} \right\vert_T \right) - pV \left. \frac{\partial V}{\partial T} \right\vert_p </math>

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T12:01:21Z

Table II

← Older revision		Revision as of 14:01, 6 October 2011
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	====internal energy====		====internal energy====

			:<math> \left. \partial H \right\vert_Q = - \left. \partial Q \right\vert_H = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) - p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial G \right\vert_Q = - \left. \partial Q \right\vert_G = -V \left( C_p - p\left. \frac{\partial V}{\partial T} \right\vert_p \right) +S \left( T\left. \frac{\partial V}{\partial T} \right\vert_p + p\left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>

			:<math> \left. \partial A \right\vert_Q = - \left. \partial Q \right\vert_A = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			====Gibbs energy function====

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T11:49:55Z

Table II

← Older revision		Revision as of 13:49, 6 October 2011
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	:<math> \left. \partial H \right\vert_Q = - \left. \partial Q \right\vert_H = -VC_p </math>		:<math> \left. \partial H \right\vert_Q = - \left. \partial Q \right\vert_H = -VC_p </math>

			:<math> \left. \partial G \right\vert_Q = - \left. \partial Q \right\vert_G = - \left( ST \left. \frac{\partial V}{\partial T} \right\vert_p -VC_p \right) </math>

			:<math> \left. \partial A \right\vert_Q = - \left. \partial Q \right\vert_A = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) + ST \left. \frac{\partial V}{\partial T} \right\vert_p</math>

			====work====

			:<math> \left. \partial U \right\vert_W = - \left. \partial W \right\vert_U = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial H \right\vert_W = - \left. \partial W \right\vert_H = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p - V \left. \frac{\partial V}{\partial T} \right\vert_p \right) </math>

			:<math> \left. \partial G \right\vert_W = - \left. \partial W \right\vert_G = -p \left( V\left. \frac{\partial V}{\partial p} \right\vert_T + S \left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>

			:<math> \left. \partial A \right\vert_W = - \left. \partial W \right\vert_A = -pS \left. \frac{\partial V}{\partial p} \right\vert_T </math>

			====internal energy====

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T11:06:22Z

Table II

← Older revision		Revision as of 13:06, 6 October 2011
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	====heat====		====heat====

			:<math> \left. \partial W \right\vert_Q = - \left. \partial Q \right\vert_W = -p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial U \right\vert_Q = - \left. \partial Q \right\vert_U = p \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial H \right\vert_Q = - \left. \partial Q \right\vert_H = -VC_p </math>

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T10:59:55Z

Table II

← Older revision		Revision as of 12:59, 6 October 2011
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	:<math> \left. \partial H \right\vert_S = - \left. \partial S \right\vert_H = -VC_p/T </math>		:<math> \left. \partial H \right\vert_S = - \left. \partial S \right\vert_H = -VC_p/T </math>

			:<math> \left. \partial G \right\vert_S = - \left. \partial S \right\vert_G = -(1/T) \left( VC_p -ST\left. \frac{\partial V}{\partial T} \right\vert_p \right) </math>

			:<math> \left. \partial A \right\vert_S = - \left. \partial S \right\vert_A = (1/T) \left( p\left( C_p \left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) + ST\left. \frac{\partial V}{\partial T} \right\vert_p \right) </math>

			====heat====

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T10:54:17Z

Table II

← Older revision		Revision as of 12:54, 6 October 2011
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	====entropy====		====entropy====

			:<math> \left. \partial Q \right\vert_S = - \left. \partial S \right\vert_Q = 0 </math>

			:<math> \left. \partial W \right\vert_S = - \left. \partial S \right\vert_W = -(p/T) \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial U \right\vert_S = - \left. \partial S \right\vert_U = (p/T) \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right) </math>

			:<math> \left. \partial H \right\vert_S = - \left. \partial S \right\vert_H = -VC_p/T </math>

	==See also==		==See also==

Carl McBride: /* Table II */

2011-10-06T10:47:14Z

Table II

← Older revision		Revision as of 12:47, 6 October 2011
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	====volume====		====volume====

			:<math> \left. \partial S \right\vert_V = - \left. \partial V \right\vert_S = 1/T \left( C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p \right)</math>

			:<math> \left. \partial Q \right\vert_V = - \left. \partial V \right\vert_Q = C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p </math>

			:<math> \left. \partial W \right\vert_V = - \left. \partial V \right\vert_W = 0 </math>

			:<math> \left. \partial U \right\vert_V = - \left. \partial V \right\vert_U = C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p </math>

			:<math> \left. \partial H \right\vert_V = - \left. \partial V \right\vert_H = C_p\left. \frac{\partial V}{\partial p} \right\vert_T + T\left. \left( \frac{\partial V}{\partial T} \right)^2 \right\vert_p - V\left. \frac{\partial V}{\partial T} \right\vert_p </math>

			:<math> \left. \partial G \right\vert_V = - \left. \partial V \right\vert_G = - \left( V \left. \frac{\partial V}{\partial T} \right\vert_p + S\left. \frac{\partial V}{\partial p} \right\vert_T \right) </math>

			:<math> \left. \partial A \right\vert_V = - \left. \partial V \right\vert_A = -S\left. \frac{\partial V}{\partial p} \right\vert_T </math>

			====entropy====

	==See also==		==See also==

Carl McBride: /* Table II */ tmp save

2011-10-06T10:33:44Z

Table II: tmp save

← Older revision		Revision as of 12:33, 6 October 2011
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	:<math> \left. \partial Q \right\vert_T = - \left. \partial T \right\vert_Q = T\left. \frac{\partial V}{\partial T} \right\vert_p</math>		:<math> \left. \partial Q \right\vert_T = - \left. \partial T \right\vert_Q = T\left. \frac{\partial V}{\partial T} \right\vert_p</math>

	:<math> \left. \partial W \right\vert_T = - \left. \partial T \right\vert_W = - p\left. \frac{\partial V}{\partial p} \right\vert_p</math>		:<math> \left. \partial W \right\vert_T = - \left. \partial T \right\vert_W = - p\left. \frac{\partial V}{\partial p} \right\vert_T</math>

			:<math> \left. \partial U \right\vert_T = - \left. \partial T \right\vert_U = T\left. \frac{\partial V}{\partial T} \right\vert_p + p\left. \frac{\partial V}{\partial p} \right\vert_T</math>

			:<math> \left. \partial H \right\vert_T = - \left. \partial T \right\vert_H = -V + T\left. \frac{\partial V}{\partial T} \right\vert_p </math>

			:<math> \left. \partial G \right\vert_T = - \left. \partial T \right\vert_G = -V </math>

			:<math> \left. \partial A \right\vert_T = - \left. \partial T \right\vert_A = p\left. \frac{\partial V}{\partial p} \right\vert_T</math>

			====volume====

	==See also==		==See also==