Figure 1.15 Schematic arrangements of a (a) heat engine; (b) heat pump or refrigerator.
The second law of thermodynamics is also stated as the law of degradation of energy whereby the quantity of energy is conserved, but its quality (the potential to produce useful work) is not. Every time energy changes form or is transferred from one system to another, its potential to produce useful work is reduced irreversibly forever. It is then said that energy has degraded.
This law is the reason we may face an energy and/or climate crisis. All the energy that we use ultimately ends up as waste heat transferred to the earth's atmosphere and then to space.
1.3.6.1 Entropy
Entropy is a thermodynamic property that is a measure of process irreversibility or energy degradation and is defined as
(1.88)
where
dS: total entropy change
ds: specific entropy change
dQ: heat transferred reversibly
T: absolute temperature at which heat is transferred
If heat is added to a system, ds will be positive (entropy increases).
If heat is removed from a system, ds will be negative (entropy decreases)
If ds = 0 during a process, the process is isentropic. The frictionless adiabatic process is an isentropic process.
A reversible process occurs when both the system and the surroundings are returned to their original conditions after the process and reverse process have been carried out. Processes in nature are irreversible, however, because reversal always causes some change to occur in the system and/or surroundings. Factors causing irreversibility include:
Friction
Unrestricted expansion
Heat transfer through a finite temperature difference
Mixing of two different gases
Chemical reactions
1.3.7 The Carnot Principle
Nicolas Sadi Carnot (1796–1832) was a French engineer who made significant contributions to the science of thermodynamics by recognising that heat engines must operate with cyclic processes. A cycle occurs when a thermodynamic system, having undergone a series of processes, arrives at a final state that is exactly the same as its initial state. In Carnot's own words (Sandfort, 1964): ‘The thermal agency by which mechanical effect may be obtained is the transference of heat from one body to another at a lower temperature’. Carnot also investigated the problem of determining the maximum work that can be extracted from the transfer of heat from high to low temperature. He eventually came up with a definition of a perfect thermodynamic engine as follows: ‘Whatever amount of mechanical effect it can derive from a certain thermal agency, if an equal amount be spent in working it backwards, an equal reverse thermal effect will be produced’. Such an engine has come to be known as the reversible engine, and the quotation as the Carnot principle. Furthermore, Carnot stated that the maximum limits of temperature between which any actual heat engine can work are the temperature of combustion of fuel and the temperature of the coldest body we can easily find and use in nature, usually the water in rivers and lakes. Figure 1.15a is the Carnot engine, and the Carnot cycle is shown in Figure 1.16 in p − V and T − s coordinates:
Process 1–2: Isothermal expansion (pV = const.) with heat addition
Process 2–3: Reversible adiabatic expansion (pVγ = const)
Process 3–4: Isothermal compression (pV = const) with heat rejection
Process 4–1: Reversible adiabatic compression (pVγ = const)
Figure 1.16 Ideal Carnot engine cycle in (a) p‐V and (b) T‐s coordinate systems.
Thermal efficiency of this heat engine is
(1.89)
Since Eq. (1.89) is obtained without reference to a specific working fluid, it can be surmised that all reversible cycles operated between the same temperatures will have the same thermal efficiency.
Based on accumulated experimental knowledge, scientists and engineers have come to the conclusion that it is impractical to build the Carnot engine, and it remains to date as the ideal cycle against which real heat engine cycles are measured. If such an engine were to operate between combustion temperature of iso‐octane (gasoline) TH = 2300 K and the standard ambient temperature TL = 298.15 K, the Carnot efficiency would be 78%. By comparison, the most efficient reciprocating internal combustion engines can hardly achieve 50%.
1.3.8 Zeroth Law of Thermodynamics
If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other and the three systems are said to be at the same temperature.
This law was added to the laws of thermodynamics early in the twentieth century because it was realised that the concept of equal‐in‐temperature is a prerequisite to a logical development of those laws. And to be logical, it was named the zeroth law of thermodynamics.
1.3.8.1 Thermodynamic Scale of Temperature
Temperature is a fundamental concept, not expressible in terms of other units or physical properties of the devices used to measure temperature, such as alcohol or mercury in glass thermometers or the electromotive force generated in a thermocouple. Physicists have established that temperature measures the kinetic energy of molecules, and the higher the molecular agitation, the higher the temperature and vice versa. The physicist William Thomson (Lord Kelvin) is credited with the establishment in 1848 of the absolute temperature scale (hence the symbol K for temperature) on the basis of Carnot's reversible cycle.
To show how it is possible to arrive at an absolute scale, a hypothetical experiment can be conducted to show that an absolute zero of temperature must exist, and then extend this line of reasoning to develop an ‘energy’ or ‘thermodynamic’ temperature scale.
It was shown earlier that the efficiency of the Carnot cycle is written as
This