Difference between Second Law Efficiency & Isentropic Efficiency in Thermodynamics
This article will give you the basic difference between Second Law Efficiency and Isentropic Efficiency in Thermodynamics. Both these concepts are very important in association with 2nd Law of Thermodynamics. The same concept is asked for many interviews including Indian Engineering Services and viva questions. The conceptual answer for the same is not available in any of the Thermodynamics textbooks. Before reading the explanation of this topic, you are advised to go through the concept of 2nd Law of Thermodynamics, Availability, and Irreversibility.
Both Second Law Efficiency & Isentropic Efficiency revolves around the same idea but is interpreted or characterized differently. Both are proportional to each other and gives a measure of the degree of irreversibility. The difference between the two can be conceptually understood by the following Temperature-Entropy diagram.
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| Fig. Illustration of Second Law Efficiency & Isentropic Efficiency |
Consider this T-S diagram. 1-2' is an Isentropic process between two pressure lines. These are drawn as a continuous line as it is a reversible process and it can be represented in a property diagram. 1-2 is the actual process which is an irreversible process and represented by dotted lines. Specific flow availability at state 1 is af1 and state 2 is af2.
With reference to the figure, the second law efficiency is defined as the ratio of actual work done to the ideal work done in the process within the state points 1 and 2. Ideal work is the work which can be obtained when irreversibility could not have been there within the fixed state points 1 and 2.
Second Law efficiency = Actual Work/ Ideal Work
Actual Work= Ideal Work - Internal Irreversibilities
Ideal Work = af1-af2 (work obtained if we discard irreversibility between 1 and 2)
However, isentropic efficiency is defined as the ratio of actual work and isentropic work in the process provided the initial state point of the process is fixed and the process is carried out isentropically.
Isentropic Efficiency = Actual Work/ Isentropic Work
Actual Work = h1-h2
Isentropic work = h1-h2'
So both of the terms illustrates the degree of departure of the irreversibility. Primarily for finding 2nd law efficiency, we have to fix two states and it is a measure of irreversibility within these 2 states. Note that, Availability ('af') is a composite function and not a state variable, but here the surroundings are fixed and for that reason, we can consider Availability as a state property. For finding isentropic efficiency, we are fixing the initial state and we are giving little relaxation to the final state so that the process occurs isentropically. Then we measure the actual variation of the work done compared to the isentropic work.
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