Thermodynamics is the branch of science which deals with the interconversion of heat and mechanical work, and the change in the properties of a system as it gains or loses energy in either form. Thermodynamics is mainly based on two empirical laws. Two system properties — internal energy and enthalpy — are associated with the first law. Another property called entropy is established as a consequence of the second law.
If a system is such that only heat can flow and work can be performed across its boundary but no matter can pass across, the system is called a thermodynamic system. The surroundings of a thermodynamic system are all other systems with which it can exchange energy. The thermodynamic properties are those characteristics of a system which describe its state. Thus, for a given amount of the gas, temperature (T), volume (V) and pressure (P) are its three thermodynamic properties. When a system simultaneously satisfies all the conditions necessary for thermal, mechanical and chemical equilibrium, no change is observed in the thermodynamic properties with time and the system is said to be in thermodynamic equilibrium. The path comprising a series of states through which the system passes to move from the initial state to the final state is called a process. If a system goes through a number of processes to eventually return to its initial state, we say that the system has gone through a cycle.
The Clausius statement of the first law of thermodynamics is:
The total energy of an isolated system remains constant whatever changes may occur within it. In mathematical terms:
Q = Δ U + W
where Q is the heat given to or withdrawn from the system, W is the work done by or on the system and ΔU is the change in internal energy of the system. All these three quantities may have positive or negative values depending on different possibilities.
A quasi-static process is one in which the properties of a system change so slowly that the deviation from thermodynamic equilibrium is infinitesimal. That is, each intermediate state through which the system passes during the process may be approximated as an equilibrium state. A quasi-static process can be plotted on a P-V, T-V or T-P diagram, while a non-quasistatic process can't be plotted.
Among the different types of molar heat capacity of an ideal gas, the molar heat capacity at constant volume, CV, and the molar heat capacity at constant pressure, CP, are of practical use. If QV is the heat required to raise temperature of n moles of a gas through ΔT at constant volume then:
QV = nCV ΔT
Similarly, if QP is the heat required to raise temperature of n moles of a gas through ΔT at constant pressure then:
QP = nCP ΔT
The relationship between these two molar heat capacities is given by Mayer's equation, which is:
CP = CV + R
Heat capacity ratio, γ, is the ratio of molar heat capacities of an ideal gas. That is:
γ = CP/CV
Kinetic theory of gases correctly predicts that, for monatomic gases, CV = 3R /2, CP = 5R /2, γ = 1.67; for diatomic gases, CV = 5R /2, CP = 7R /2, γ = 1.40; for polyatomic gases, CV = 3R, CP = 4R, γ = 1.33.
There are various types of quasi-static thermodynamic process, depending on which quantity remains constant and which quantities vary during the process. In an isothermal process, temperature remains constant while pressure and volume vary. In an isochoric process, volume remains constant while temperature and pressure very. In an isobaric process, pressure remains constant while temperature and volume vary. In an adiabatic process, no heat flows in or out of the system while temperature, volume and pressure all vary. We shall derive important results for Q, Δ U and W for each of the processes mentioned above in due course.
The Kelvin-Planck statement of the second law of thermodynamics is:
It is impossible to remove thermal energy from a system at a single temperature and convert it into an equivalent amount of mechanical work without changing the system or the surroundings in some other way.
From an engineering point of view, the most important application of the second law is the limited efficiency of heat engines. A heat engine is a device which continuously converts thermal energy into mechanical work. The thermal efficiency of a heat engine is the ratio of the work done by the engine to the heat absorbed by it from the hot reservoir. Notable examples of heat engine are steam engine and internal combustion engine. There are two types of internal combustion engine: spark ignition engine such as a petrol engine and compression ignition engine such as a diesel engine. The diesel engine has the highest thermal efficiency.
A process which can advance only in forward direction is called an irreversible process. But if a process, operated backwards, takes the system through the same equilibrium states in the reverse order, the original process is known as a reversible process. If a process has to be reversible, it must be quasi-static, non-dissipative and any transfer of heat must take place isothermally. A heat engine cycle which consists only of reversible processes is called a reversible cycle, and the engine is called a reversible engine. In 1824, French physicist Sadi Carnot showed that a reversible engine is the most efficient of all heat engines. Such an engine is known as a Carnot engine, and the cycle followed by it is called Carnot cycle. The formal statement of Carnot theorem is:
No heat engine operating between two given heat reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.
Carnot efficiency, which is the thermal efficiency of a Carnot engine, is given by the formula:
ηC = 1 - Tc/Th
Here Tc and Th are the temperatures of the cold and hot reservoirs respectively. The result is independent of the working substance used in the engine!
When a heat engine is run in reverse, heat is transferred from the cold reservoir to the hot reservoir and work must be performed on the system. This is the mode of operation of a refrigerator or a heat pump. A Carnot engine run in reverse is called a Carnot refrigerator. Just like Carnot engine, a Carnot refrigerator has the highest coefficient of performance or COP operated between two fixed temperatures.
A common feature of all irreversible processes is that they take the system plus the surroundings towards greater disorder. The concept of entropy, S, was first introduced by Rudolf Clausius. It is an extensive thermodynamic property which gives the measure of a system's disorder. The unit of entropy is joule per kelvin (J/K).