

§ 6 Entropy
Thermodynamic entropy and its meaning:
Entropy  is a function of the system, an infinitesimal change in a reversible process which is the ratio of the infinitesimal amount of heat introduced into the process, to the temperature at which it was introduced. All in a reversible process the entropy change can be calculated by the formula:
where the integration is one of the initial state 1 of the system to the final state 2. In any reversible process the change in entropy is equal to 0 (1) 2) In thermodynamics, it is proved that the system undergoes irreversible S cycle increases ΔS> 0 (2) Equations (1) and (2) apply only to closed systems, but if the system is exchanged heat with the environment, its S can behave in any way. Of (1) and (2) can be written as the Clausius inequality ΔS ≥ 0 ie entropy of a closed system can either increase (in the case of irreversible processes) or remain constant (in the case of reversible processes). If the system performs the equilibrium transition from state 1 to state 2, the entropy change
where dU and δA is recorded for a particular process. According to this formula ΔS is determined up to an additive constant. The physical meaning is not the entropy, entropy difference. We find the entropy change in the process of an ideal gas.
ie changes in the entropy S ΔS_{1 →}_{ 2} ideal gas at its transition from state 1 to state 2 is independent of the process. Because for an adiabatic process δQ = 0, ΔS = 0 => S = const, ie adiabatic reversible process takes place at constant entropy. So it is called isentropic. An isothermal process (T = const; T_{1} = T_{2}: )
When isochoric process (V = const; V_{1} =V_{2}; )
Entropy is additive: the entropy of the system is the sum of the entropies of bodies in the system. S = S_{1} + S_{2} + S_{3} + ... Qualitative difference of the thermal motion of molecules from other forms of movement is its state of chaos, randomness. Therefore, to characterize the thermal motion to introduce a quantitative measure of the degree of molecular disorder. If we consider any given macroscopic state of the body with some average values, then it is nothing but the continuous change of close microstates differing distribution of molecules in different parts of the volume and the energy is distributed between the molecules. These continuous successive microstates characterizes the degree of disorder of the macroscopic state of the entire system, ϖ is called thermodynamic probability of the microstate. Thermodynamic probability ϖ of the system  is the number of ways that this can be done state macroscopic system, or the number of microstates carrying this microstate (ϖ ≥ 1, and the mathematical probability of ≤ 1). According to Boltzmann, the entropy S of the system and the thermodynamic probability linked as follows:
where k  Boltzmann constant, . Thus, the entropy is defined logarithm of the state in which this can be achieved microstate. Entropy can be considered as a measure of the probability of the state thermodynamic system. Boltzmann formula allows us to give the following statistical interpretation of entropy. Entropy is a measure of disorder in a system. In fact, the greater the number of microstates realizing this microstate, the greater the entropy. In the equilibrium state of the system  the most probable state of the system  the maximum number of microstates, with the maximum and entropy. Because real processes are irreversible, it can be argued that all the processes in a closed system leads to an increase in its entropy  the principle of entropy increase. In the statistical interpretation of entropy, this means that the process in a closed system are to increase the number of microstates, in other words, from less probable to more probable, as long as the probability of the state will not be maximized.
2) ΔS ≥ 0 (S = 0 for a reversible and ΔS ≥ 0 for an irreversible process) 3) According to Kelvin: circular process is not possible, the only result of which is the conversion of heat received from the heater into an equivalent work. 4) In the Clausius: circular process is not possible, the only result is to transfer heat from the less heated body to a warmer. To describe the thermodynamic systems at 0 K using Theorem NernstPlanck (third thermodynamics): the entropy of all bodies in equilibrium tends to zero as the temperature approaches 0 K
From Theorem NernstPlanck equation, it follows that C_{p} = C_{v} = 0 at 0 K.
Carnot cycle and its efficiency
Thermostat  is thermodynamic system that can exchange heat with the bodies without a change in temperature. The principle of operation of the heat engine: the thermostat with temperature T_{1}  heater for a cycle is subtracted the amount of heat Q_{1}, a thermostat with temperature T_{2} (T_{2} < T_{1}), refrigerator, for a series of heat transferred to Q_{2}, while work is done A = Q_{1}  Q_{2}
Circular process or cycle is a process by which the system is going through a number of states, is reset. Cycle in the state diagram depicted a closed curve. Cycle, performed by an ideal gas can be divided into processes of expansion (12) and compression (21), the work of expansion is positive A_{12} > 0, because V_{2}> V_{1}, the work of compression is negative A_{12} < 0, because V_{2} < V_{1}. Hence, the work done by the gas per cycle, determined by the area covered by a closed curve 121. If the cycle is done positive work loop clockwise), then the cycle is called direct if  reverse cycle (cycle occurs in a counterclockwise).
that is, the work done per cycle is the amount of heat received from the outside, but Q = Q1  Q2 Q_{1}  the amount of heat received by the system Q_{2}  the amount of heat given system. Thermal efficiency for cyclic process is the ratio of the work done by the system, to the amount of heat supplied to the system:
To η = 1, the condition Q_{2} = 0, ie, heat engine should have one heat source Q_{1}, but this contradicts the second law of thermodynamics. The reverse process is happening in the heat engine is used in the refrigeration machine. The thermostat with temperature Т_{2} deducted the amount of heat Q_{2} transferred to the thermostat and the temperature T_{1}, the amount of heat Q_{1}. Without doing the work can not take away the heat from a hot body, and at least give it a warmer. Based on the second law of thermodynamics, Carnot led theorem. Working body  the body to make circular process to exchange energy to other bodies. 12isothermal expansion at T_{1} heater, gas is supplied to the heat Q_{1} and work is done
2  3  adiabats. expansion, the gas does work A_{23}_{ }> 0 on external bodies. 3  4isothermal compression at T_{2} refrigerator, heat is taken Q_{2} and work is done
41adiabatic compression work is done on the gas A_{41}_{ }< 0 external bodies. _{} Adiabatic expansion Q_{23 }= 0, and the work done A_{23} gas by the internal energy A_{23 }= U
The amount of heat Q_{2}, uploaded from gas to refrigerator at isothermal compression equal to the work of compression А_{34}
The work of the adiabatic compression
The work performed by a circular process
and equal to the area of ??the curve 12341. Thermal efficiency Carnot cycle
From the equation for adiabatic processes 23 and 34 we obtain
then
ie efficiency Carnot cycle is determined only by the temperature heater and refrigerator. To increase the efficiency necessary to increase the difference Т_{1}  Т_{2}.
