1.2.3 Second law of thermodynamics: There are two statements of second law of thermodynamics.
Clausius statement: It is impossible to construct a system which will operate in a cycle, transfers heat from the low temperature reservoir (or object) to the high temperature reservoir (or object) without any external effect or work interaction with surrounding.
Kelvin Plank statement: It is impossible to construct a heat engine which produces work in a cycle while interacting with only one reservoir.
Kelvin Plank statement necessarily states that Perpetual Motion Machine of second kind is impossible. These statements introduce a new property termed as entropy which is the measure of disorder.
There are some corollaries of second law of thermodynamics
- All the reversible heat engines working between same temperature limits have same efficiency.
- Irreversible heat engine working in the same temperature limit as the reversible heat engine will have lower efficiency.
The second law of thermodynamics leads to an inequality called as Clausius inequality which is valid for general process happening in any system. This law grades the energies according to which work is high grade energy and heat is low grade energy. Therefore second law of thermodyanamics directs that low grade energy can not be complety converted into high grade energy. This law also states the possibility of having a process in reality unlike the first law which can at most quantify the effects of the process if process becomes a reality. Hence according to second law only those processes are possible in which entropy of the universe increase or atleast remains constant. This is called as entropy increase principle which also states that entropy of an isolated system always increases or remain constant.
1.2.4 Third law of thermodynamics: ‘Entropy of pure substance in thermodynamic equilibrium is zero at absolute zero temperature’. Therefore according to this law, there exists zero Kelvin temperature on the temperature scale but it is difficult to achieve the same.
1.3. Isentropic relations:
Isentropic relations are the relations between thermodynamic properties if the system undergoes isentropic process.
Consider a closed system interacting dQ amount of energy with the surrouding. If dU is the change in internal energy of the system and pdV is work done by the system against pressure p due to volume change dV. According to First Law of Thermodynamics we know that,
dQ = dU + pdV
From Second law of Thermodynamics,
dQ = TdS
Here dS is the entropy chage due to reversible heat interaction dQ.
Therefore, combining First and Second Laws of Thermodynamics,
TdS = dU + pdV |
(1.1) |
However, we know that, if H is enthalpy of the system then,
H = U + pV |
(1.2) |
Combining equations 1.1 and 1.2 we get,
TdS = dH - Vdp
For system with unit mass of matter, above equation can be written as,
Tds = dh - vdp |
(1.3) |
Here s, h and v are specific entropy, enthalpy and volume respectively.
Speciality of equation 1.3 is, its usefullness to calculate entropy change of any reversible process as below,
where, dh = Cp dT and for calorifically perfect gas Cp (Specific heat at constant pressure) is assumed to be constant,
Integrating above equation from starting state 1 to end state 2 of the process which system has undergone
