The subscript "actual"refers to the actual process(which is irreversible). The entropy change associated with the state change is ds dActhal dWrey-dwactual (C.5.1) If the process is not reversible, we obtain less work(see IA W notes) than in a reversible process, dWtol dWv, So that for the irreversible process T There is no equality between the entropy change ds and the quantity d@/Tfor an irreversible process. The equality is only applicable for a reversible process The change in entropy for any process that leads to a transformation between an initial state"a and a final state“b” is therefore e deactual is the heat exchanged in the actual process. The equality only applies to a reversible process The difference dwrey-dWactual represents work we could have obtained, but did not. It is referred o as lost work and denoted by Wost. In terms of this quantity we can write ds= de (C.5.3) The content of Equation(C.5.)is that the entropy of a system can be altered in two ways: (i) through heat exchange and (ii) through irreversibilities. The lost work( dost in equation C5.3)is always greater than zero, so the only way to decrease the entropy of a system is through heat transfer To apply the second law we consider the total entropy change( system plus surroundings). If the surroundings are a reservoir at temperature t, with which the system exchanges heat reservoir surroundings= ctual The total entropy change is 1C-91C-9 The subscript “actual” refers to the actual process (which is irreversible). The entropy change associated with the state change is dS dQ T T =+ − actual [ ] dW dW rev actual 1 . (C.5.1) If the process is not reversible, we obtain less work (see IAW notes) than in a reversible process, dW dW actual < rev , so that for the irreversible process, dS dQ T actual > . (C.5.2) There is no equality between the entropy change dS and the quantity dQ/T for an irreversible process. The equality is only applicable for a reversible process. The change in entropy for any process that leads to a transformation between an initial state “a” and a final state “b” is therefore ∆SS S dQ T b a actual a b =−≥ ∫ where dQactual is the heat exchanged in the actual process. The equality only applies to a reversible process. The difference dW dW rev − actual represents work we could have obtained, but did not. It is referred to as lost work and denoted by Wlost . In terms of this quantity we can write, dS dQ T dW T actual lost = + . (C.5.3) The content of Equation (C.5.3) is that the entropy of a system can be altered in two ways: (i) through heat exchange and (ii) through irreversibilities. The lost work ( dWlost in Equation C.5.3) is always greater than zero, so the only way to decrease the entropy of a system is through heat transfer. To apply the second law we consider the total entropy change (system plus surroundings). If the surroundings are a reservoir at temperature T, with which the system exchanges heat, dS dS dQ T reservoir surroundings actual ( ) = = − . The total entropy change is dS dS dS dQ T dW T dQ T total system surroundings actual lost actual =+ = +     −