Chapter 3 The 2nd law of thermodynamics 1st law : Any thermal process should obey the law of energy conservation！ Is a process possible if it obeys the law of energy conservation?

Heat transfer High temperature Low temperature Conversion of work into heat work heat

Gas expansion uniform in density non-uniform in density Life process birth death All the real processes in nature related to thermal phenomena should have directions. 2nd law a basic law about the direction of a process

§1 The literal statements of the 2nd law The Kelvin statement No process is possible whose sole result is the absorption of heat from a single reservoir and the complete conversion of this heat energy into work without producing any other effects in the environment. perpetual motion machine of type II is impossible Conversion of work into heat is irreversible

The Clausius statement No process is possible whose sole result is the transfer of heat from a cold to a hot body without producing any other effects in the environment. A refrigerator is not possible without using work Heat transfer is irreversible

If Kelvin statement fails Clausius statement fails =

If Clausius statement fails Kelvin statement fails =

Equivalence of Clausius and Kelvin statements! Irreversibility of converting work into heat Irreversibility of heat transfer All the irreversibility are consistent! All the irreversible processes are related and can be derived to each other, which implies that there may be various statements of the 2nd law and all of them are equivalent. The irreversibility is not determined by the path of a process but by the initial and final states of the system, i.e., it is a function of state (entropy).

§2 Carnot theorem and entropy Carnot’s theorem The literal statements The efficiency of an irreversible heat engine operating between two reservoirs (hot and cold) is less than that of any reversible engine operating between the same reservoirs. The mathematic expressions

perpetual motion machine of type II Prove perpetual motion machine of type II if = R

The Clausius relations Cyclic process with two reservoirs If the minus sign is put into Q2, then By writing so, Q1 and Q2 are the heat “absorbed” from reservoirs with temperature T1 and T2, respectively. Cyclic process with many reservoirs

Prove … … R R R … … system

Cyclic process with many reservoirs General cyclic process For reversible cycle A entropy B can take any reversible process extensive state quantity For irreversible cycle The principle of increase of entropy

§3.3 The principle of increase of entropy For irreversible cycle A B mathematic expression of 2nd law Note：In a reversible process, T can be viewed as the temperature of the system, while it is not in an irreversible process.

1st law ＋ 2nd law The principle of increase of entropy For an adiabatic system It follows that in an adiabatic process the entropy of a system never decreases. It either increases for irreversible process or remains constant for reversible process. To determine the direction of an irreversible process

§4 Calculation of entropy change Reversible process adiabatic process isothermal process constant-volume process constant-pressure process phase transition Irreversible process Entropy is a function of state! Consider a virtual reversible process with the same initial and final states

§5 Temperature-entropy plot Reversible process： Using T～S plot to calculate heat absorbed: Using T～S plot to calculate the efficiency of a cyclic process： ratio of the area!