State variables in thermodynamics.

What exactly is a state variable in thermodynamics? I have heard that temperature is a state varibale because we are not interested in how this state is achieved but how is the work done by a system not a state variable? also, the book I'm having says that

"the difference between 2 quantities which are now state variabales is a state variable itself."

what exactly does it mean? The book only has one paragraph dedicated to this. And I'm confused now.
Heat(or work) is not a state variable because heat is not a property of an object but rather a quantity that's associated with an incident of a *change* of states (i.e. temperature). Heat "flows" from one object to another, so heat does not belong to any objects, but it belongs to the phenomenon (of temperature changes).

"The temperature of the sphere is 300K." is a valid statement, but "The heat of the sphere is 40J" is not.
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Same thing with work... work is "done" from one object to another, just like heat "flows" from one to another. Temperature does not "flow" or "be done"... it just takes some value all the time. By contrast, work and heat are something that pop up when an event associated with the variable occurs.

What your book says is I think, that if A and B are state variables, A - B is a state variable as well.
Hmmm i somewhat gettit. Mathematically can we say, for the temperature of a system, we can't put it as -ve something. But the heat in a system can be said to be negative if it actually loses heat. Can it be looked at it this way?

oh and about the statement in the book, i typed it wrongly, it should bem

"the difference between 2 quantities which are NOT state variabales is a state variable itself."


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Looks familiar, I've always gotten them as the variables which essentially define the state of a thermodynamic system, such as temperature, volume, pressure etc. So essentially they are the principal variables of state eqs, whatever that may be then. I've always found the difference between state and internal variables a bit puzzling, i.e. internal variables whether they are or are not state variables ... I suppose typically I go by the former definition.

James R

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A state variable is one which can be used to characterise the system. For example, the state of a fixed mass of an ideal gas can be characterised by any two state variables chosen from the following list:

Gibbs energy
Helmholtz energy
Internal energy

If you know the values of any two of these quantities, you can work out all the others, and you know everything there is to know about the macroscopic state of the gas.

The statement about two non-state variables giving a state variable is probably a reference to the first law of thermodynamics, which relates changes in the internal energy of a system (a state variable) to heat flow and work done (both non-state variables).

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