Cycle entropy change

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

Because the engine operates in cycles, it experiences no change in its own properties therefore the total entropy change of the engine and its associated heat reservoirs is given by equation 8 ... 

In a Carnot s cycle, the entropy Qi/Ti is taken from the hot reservoir, and the entropy Q2/T2 is given up to the cold reservoir, and no other entropy change occurs anywhere else. Since these two quantities of entropy are equal and opposite, the entropy. change in the hot reservoir is exactly balanced, or, to use an expression of Clausius, is compensated by an equivalent change in the cold reservoir. Again, in any reversible cycle there is on the whole no production of entropy so that all the changes are compensated. 

Forster s cycle (50MI1) (method 1 in Table VIII, also known as the thermodynamic method ). This cycle is particularly important because it can be used even when the protolytic equilibrium is not reached in the excited state. On the other hand, it has two important limitations (i) the frequencies of the 0-0 transitions in absorption or emission are necessary and (ii) ionization entropy changes are assumed to be the same in the ground and in the excited states. The experimental difficulties involved in determining the 0-0 transition frequencies have led to the use of the frequencies of the absorption maxima (procedure a), emission maxima (procedure b), or the average therefrom (procedure c). 

Figure 4.2 Standard Gibbs energy, standard enthalpy and standard entropy cycles for the reaction between hydrated protons and hydrated electrons to give gaseous dihydrogen Gibbs energy and enthalpy changes are in units of kJ mol- the entropy changes are in units of J K 1 mol-1...

A The cycle of Figure 6.1 suggests that the equation giving the j entropy change for reaction (6.7) is, when combined with the result of Worked Problem 6.3 ... 

However, according to statement 1 a of the second law, Q v cannot be directed into the system, for the cycle would then be a process for the complete conversion of heat into work. Thus, j dQnv is negative, and it follows that SA - SB is also negative whence SB > SA. Since the original irreversible process is adiabatic, the total entropy change as a result of this process is AStota, = SB - SA > 0. 

Ideal gas, 61, 63-77 Carnot cycle for, 145-147 equation of state for, 64 entropy changes for, 152-155 fugacity of, 327, 334 heat capacity of, 64-68, 107-113 internal energy and enthalpy changes for, 64-77... 

Forster cycle Indirect method of determination of excited state equilibria, such as pK values, based on ground state thermodynamics and electronic transition energies. This cycle considers only the difference in molar enthalpy change (AAH) of reaction of ground and excited states, neglecting the difference in molar entropy change of reaction of those states (AAS). 

Thus, is the integration of t/g(rev)/T during the first part of the cycle and so is Q2IT2 for the third part of the cycle. So these values are, in fact, entropy changes of the system... 

Let S be the entropy and be the reversible heat added. In a given differential step, the heat added is dQ The differential change in entropy in every differential step is therefore dS = dQ JI. Around the cycle, the change in entropy is the integral, thus... 

The thermochemical cycle in Scheme 3 was used for this purpose for the Mn, Mo, and Fe dimers. The formal potentials E° (M2/2M ) were derived from equilibrium constant measurements of the redox equilibria, Eqs 26 and 27, by use of suitable reducing agents. When these formal potentials were combined with the anion oxidation potentials, the M-M BDEq could be calculated from Eq. 28 as 117 kJ moE for Mn2(CO)io, 92 kJ mol for Cp2Mo2(CO)e, and 105 kJ moE for Cp2Fe2(CO)4. For the Mn dimer, estimates for the entropy change were available and eventually led to an estimated Mn-Mn BDE of ca 159 kJ moE in enthalpy terms. 

By analyzing the Carnot cycle description of macroscopic energy transfer processes, Clausius demonstrated that the quantity J(l/T)dqrev is a state function, because its value for any reversible process is independent of the path. Based on this result, Clausius defined the procedure for calculating the entropy change AS = Sf — S for a system between any thermodynamic states i and f as... 

---