Notation of thermodynamics & heat

[gop]

Hi,

I have two questions regarding the laws of thermodynamics

1) For example in http://en.wikipedia.org/wiki/First_law_of_thermodynamics the first law of thermodynamics is defined using two different symbols d (as in infinitestimal change) und the symbol delta (which in the article also represents infinitestimal change). Why are there (sometimes) those two different symbols used?

2) Is there a way heat can be measured or is it better to think of it as an abstract quantity of energy transfer (induced by temperature differences).

thx

 

[Andrew Mason]

Hi,

I have two questions regarding the laws of thermodynamics

1) For example in http://en.wikipedia.org/wiki/First_law_of_thermodynamics the first law of thermodynamics is defined using two different symbols d (as in infinitestimal change) und the symbol delta (which in the article also represents infinitestimal change). Why are there (sometimes) those two different symbols used?

The differential form of the first law, dQ = dU + dW applies to infinitessimal changes (ie. an infinitessimal part of a process). The form with the Deltas relates to a finite change. The form: \Delta Q = \Delta U + W is a simpler way of stating:

\int_a^b dQ = \int_a^b dU + \int_a^b dW where a and b are the beginning and end states of a process.

2) Is there a way heat can be measured or is it better to think of it as an abstract quantity of energy transfer (induced by temperature differences).

It is not an abstract quantity. To measure it determine the work done and the changes in internal energy and add them together to get the heat flow.

If you had some way of measuring the heat flow from/to the reservoirs that are supplying or receiving the heat flow from the system (by measuring the change in internal energy of the reservoir: temperature change x mass x specific heat), you could measure that.

AM

 

[qbert]

1. We use two symbols because there are two different kinds of "infinitesimal change".

There are really two types of quantities here. The internal energy is the differential of a state function. we use the notation dU to remind us of that fact. For finite changes the change in internal energy depends only on the starting and ending states.

Heat and work are "inexact differentials". Meaning there is NO function such that the value of the function is the heat or the work. We use a different notation to remind us of that fact. For finite changes the amount of Heat absorbed (or released) depends on the exact path [the precise way we move from the initial to the final state].

 

[Andrew Mason]

1. We use two symbols because there are two different kinds of "infinitesimal change".

There are really two types of quantities here. The internal energy is the differential of a state function. we use the notation dU to remind us of that fact. For finite changes the change in internal energy depends only on the starting and ending states.

Heat and work are "inexact differentials". Meaning there is NO function such that the value of the function is the heat or the work.

What about: W = \int PdV ?

AM

 

[pabloenigma]

W is not a state function.and the differential of W is not the differential of a state function.thats what its meant my W and q being inexact differentials

 

[Zeppos10]

A lot of trouble is caused in thermodynamics by a kinf of 'chronofobia' ie the avoidance of using time explicitly in equations. If one writes the first law as dU/dt = q+w [J/s] and the integral as ∆U= Q+W [J], where it is understood from day1 (this is not the case now) that work and heat are inputs, HENCE are not variables of state, then a lot of this d-trouble could be avoided.
Note that in the thermodynamic literature at least 5 different d-operators are used, invluding a variational d (d~) and a 'not-a-normal-differential' d (d-). Confusion galore.

 

[gop]

So as an mathematical analogy one could say that dU is an exact differential form while delta Q and delta W are not exact (differential forms).

 

[Zeppos10]

So as an mathematical analogy one could say that dU is an exact differential form while delta Q and delta W are not exact (differential forms).

I do not see any 'analogy':
dU/dt= q+w is a balance-equation (for energy). After some substitutions that imply serious limititations, the equation dU=TdS-pdV results, which is TAKEN to be an exact differential. The first equation is not an exact differential as far as I can see.
(Note that a swimmingpool with 'water-level' as a single variable of state can have a water-balance equation with more then one input/output.)