Chronology |
Current Month |
Current Thread |
Current Date |

[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |

*From*: John Denker <jsd@av8n.com>*Date*: Mon, 11 Jan 2010 03:05:04 -0700

On 01/10/2010 09:19 PM, LaMontagne, Bob wrote:

... The equation T ds = du + Pdv is a standard state variable

equation for a control mass. I thought it was a universal equation

that was not tied to a particular process, but maybe that's where my

thinking is wrong.

There's definitely a problem there. The equation

mentioned above falls into the category of being

only sometimes true.

Tangential remark: That's why my little quiz was

not a T/F quiz but rather a T/N quiz, where

T means "reliably true" and

N means "not reliably true" which includes things

that are only sometimes true.

The aforementioned equation can be rewritten as

dE = T dS - P dV [1]

and if we write it that way we ought to be able to

get past all questions of terminology, notation, and

interpretation ... and focus on the meaning.

Even so, the meaning of equation [1] is not universally

true ... and it is certainly not the best way to express

the first law of thermodynamics. For multiple practical

as well as pedagogical reasons, the first law should

be stated as

_Energy obeys a strict local conservation law._

That's it. Pure and simple.

If/when the energy can be expressed as a function of

V and S alone, and is differentiable, then equation [1]

follows immediately. It must be emphasized that this

equation does not express conservation of energy. It

does not depend on the fact that energy is conserved;

it only requires that energy be a differentiable function

of state. A similar equation applies to any other

differentiable function of state, including things like

the temperature and molar volume, which are obviously

not conserved. For more on this, see the newly revised

and reorganized section:

http://www.av8n.com/physics/thermo-laws.htm#sec-state-function

In the case where electricity is flowing, the energy

is definitely not a function of V and S alone, so

equation [1] needs to be repaired. If energy can be

expressed as a function of V, S, and charge (which

might make sense for a battery) then we can immediately

write

dE = T dS - P dV - voltage d(charge) [2]

Tangential remark: The minus signs in equations [1]

and [2] are somewhat arbitrary. The choices shown

here are conventional, although the conventions

changed in the not-too-distant past.

To say more-or-less the same thing in another way, you

need to make sure that your notion of thermodynamic

state includes enough components to span the state

space. If you leave off one of the variables, then

E and all the other things that are supposed to be

functions of state won't be functions of state.

Your state vector needs many enough components to

span the entire space, and few enough components

so that they are linearly independent.

When you expand the gradient vector as in

equation [1] or equation [2], there will be one

term on the RHS for each dimension, i.e. one for

each component of the state vector.

**References**:**[Phys-l] Thermodynamics question***From:*"LaMontagne, Bob" <RLAMONT@providence.edu>

**Re: [Phys-l] Thermodynamics question***From:*"Bob Sciamanda" <treborsci@verizon.net>

**Re: [Phys-l] Thermodynamics question***From:*"LaMontagne, Bob" <RLAMONT@providence.edu>

**Re: [Phys-l] Thermodynamics question***From:*"Bob Sciamanda" <treborsci@verizon.net>

**Re: [Phys-l] Thermodynamics question***From:*"LaMontagne, Bob" <RLAMONT@providence.edu>

- Prev by Date:
**Re: [Phys-l] Thermodynamics question** - Next by Date:
**Re: [Phys-l] Separating inertial mass and g mass. Was: Re: adifferent kind of math background quiz** - Previous by thread:
**Re: [Phys-l] Thermodynamics question** - Next by thread:
**Re: [Phys-l] Thermodynamics question** - Index(es):