Eduard-Job-Stiftung für Thermo- und Stoffdynamik

Entropieerzeugung in einem Entropiestrom

Heat Conductor

Entropy Transfer and Energy
If an amount of entropy S is moved from a place l at the temperature T1 to another at the temperature T2, the potential energy E of the entropy is lowered by:

Since energy is conserved (First Law), but entropy can be created (Second Law) the loss in potential energy can be compensated by entropy SG generation.

ST = SG + S is the amount of entropy finally arriving at the second place. By definition T1 is larger than T2 and therefore SG > 0. The flow of entropy along a temperature gradient always creates new entropy, or in other words, entropy can create itself.


 

Heat Conduction from the Energetic Point of View
The heat conductor is divided into n uniform pieces with the length x and the cross-sectional area A and Ti is the temperature of a piece. i can vary between 0 and n+1, where T0 is the temperature of the gas and Tn+1 the temperature of the calorimeter. The flux of heat energy WT in a slab of the conductor is described with the following equation:

is thermal conductivity of the heat conductor at the bottom of the piston. The following assumptions were made to use this equation for the simulation:

  1. The slab is so thin, that equals .
  2. has the same value at every point of the cross-section A.
  3. The surface of the heat conductor has the same temperature than the gas in the piston at one end and at the other the temperature of the calorimeter.

These assumptions allow us to write:

At one end of the piece thermal work is done on the slab, while it performs thermal work on its neighbour at the other end. The difference between both works is the thermal work changing the properties of the slab. for k-th slab of the conductor in the time interval can be calculated as follows:

This thermal work is used to heat up the piece:

is the specific heat capacity and its density.

Since WT is a conserved quantity on heat conduction, the entropy change at every place of the heat conductor can be easily calculated.

Entropy flux from the piston into the conductor
Entropy change in the heat conductor
Entropy flux from the conductor into the calorimeter

Heat Transfer from the Entropic Point of View
Heat conduction can be regarded as an entropy flow from a hot place to a colder one.

   and    

The same reasoning as done in the previous sections leads to the following equations for the change of the entropy content of single slab from the heat conductor and for the corresponding temperature change .

   and    

The choice of the set equations for the description of the heat transfer depends on the aim of the simulation. Currently, the program does not calculate the entropy change in a slab of the heat conductor . The first set of equations was chosen, because the calculation of is not necessary in this approach and the the calculation of = not requested, which reduces the number of divisions per simulation step.