Steady-State,
First Law of Thermodynamics (Energy Balance Method).
This simple example illustrates the use of the first law of thermodynamics in the presence of fields (in the form of Equation (8)).The first law is applied in conjunction with the principle that, at equilibrium, d[??] must be independent of the position within the system, where the change takes place.
The first law of thermodynamics in the presence of fields states that the change in the field-dependent internal energy, [??], of the system is equal to the sum of the field-dependent work, IV, and heat, [??], delivered at the boundaries or directly to the contents of the system, and the change in the interaction energy, [psi], due to changes in the source of the field.
From (25), it can be analyzed that the
first law of thermodynamics remains valid for the following particle creation rate:
Applying the
first law of thermodynamics on the event horizon and using the usual entropy-area relation, we have derived the Friedmann equations the same as the ones obtained via other approaches.
The
first law of thermodynamics is based on the concept that energy remains conserved in the system but can change from one form to another.
Unified
First Law of Thermodynamics. Applying the Misner-Sharp mass/energy [E.sub.MS] := (Y/2G)(1 - [h.sup.[alpha][beta]][[partial derivative].sub.[alpha]]Y[[partial derivative].sub.[beta]]Y) [26,27] to be the effective energy [E.sub.eff] and substituting [h.sub.[alpha][beta]] = diag[-1, [a.sup.2]/(1 - k[r.sup.2])], one obtains
Einstein's equation can be derived from the thermodynamics [13]; on the other side, the thermodynamic route to the gravity field equation, which could get the
first law of thermodynamics in Einstein gravity, was proposed by Padmanabhan [14-16].
Dehghani, the authors tackled the unified
first law of thermodynamics and its genuine connection with the apparent horizon of FRW universe in which they found that whenever there is no energy exchange between the various parts of cosmos, one could get an expression for the apparent horizon entropy in quasi-topological gravity.
In Section 3, we calculate the thermodynamical quantities, check the
first law of thermodynamics, and study the phase transitions of the black hole in extended phase space.
This approach soon generalized to the cosmological situation, where it was shown that, by applying the Clausius relation to the apparent horizon of the Friedmann-Robertson-Walker (FRW) universe, the Friedmann equation can be rewritten in the form of the
first law of thermodynamics [21].
In Section 3, we use the Einstein field equations in Lyra manifold as well as the unified
first law of thermodynamics in order to obtain the generalization of the Misner-Sharp mass [63] in this theory.