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1. ⦿ Th e E n t r o p y is a the r mod y nami c p r opert y o f a working substance and serves as a valuable tool in the second law analysis of engineering devices. ⦿ Entropy is a function of a quantity of heat which shows the possibility of conversion of that into work. ⦿ Entropy is a thermodynamic property; it can be viewed as a measure of disorder i.e. More disorganized a system the higher its entropy.

2. ⦿ The Clausius Theorem is a mathematical explanation of the Second Law of Thermodynamics. ⦿ Also referred to as the “Inequality of Clausius”, the theorem was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. ⦿ The Clausius Theorem was first published in 1862in Clausius’ sixth memoir, “On the Application of the Theorem of the Equivalence of Transformations to Interior Work”.

3. ⦿ “ When a system undergoes a complete cyclic of around the cycle is less process, the integral than zero.” ⦿ M a them a ti c ally : ( ) ≤ ⦿ δ Q is energy flow into the system due to heating and T being absolute temperature of the body when that energy is absorbed. ⦿ The following equation must be found true for any cyclical process that is possible, reversible or not.

4. ⦿ Consider a reversible engine R and irreversible engine I working between two thermal reservoirs at temperatures T H and T L . ⦿ Efficiency of reversible engine is : where δQ H = heat added, δQ L = heat rejected. ⦿ Efficiency of irreversible engine is : ⦿ We know that efficiency of reversible engine is more than that of irreversible engine under same temperature limit. ∴ η R > η I ∴ ( ) R > ( ) I ∴ ( ) R > ( ) I ( ∵ for reversible engines )

5. ⦿ ∴ ( ) < ( ) I ⦿ ∴ ( ) I < ( ) I ⦿ ∴ ( ) I - ( ) I < ⦿ We know that, heat added ( δQ H ) should be positive and heat rejected( δQ L ) should be negative. ⦿ ∴ ( ) I - (- ) I <

6. ⦿ ∴ ( ) I + ( ) I < ⦿ Considering complete original irreversible cycle : ⦿ ∴ ⦿ ∴ ∮ ( ) < for an irreversible cycle. ⦿ According to Clausius Theorem ∮ = for reversible cycle. ⦿ Combining results for reversible and irreversible cycle, we get : This expression is known as Clausius Inequality .

7. On a T-S diagram, the area under the process curve represents the heat transfer for internally reversible processes .

8. δ Q int, rev = T dS Q int, rev = Q int, rev = T ΔS δ q int, rev = T ds q int, rev = q int, rev = T Δs

9. Mollier diagram: The h-s diagram For adiabatic steady-flow devices, the vertical distance Δh on an h-s diagram is a measure of work, and the horizontal distance Δs is a measure of irreversibility's.