3)There exists a property called entropy, S, which is a thermodynamic property of a system. For a reversible process, changes in this property are given by ds=(do T The entropy change of any system and its surroundings, considered together, is positive and approaches zero for any process which approaches reversibility Atotal≥0 For an isolated system, i.e., a system that has no interaction with the surroundings, changes in the system have no effect on the surroundings. In this case, we need to consider the system only, and the first and second laws become AE system=0 △S >0 For an isolated system the total energy (E=U+ Kinetic Energy Potential Energy +...)is constant The entropy can only increase or, in the limit of a reversible process, remain constant All of these statements are equivalent, but ( 3)gives a direct, quantitative measure of the departure from reversibility Entropy is not a familiar concept and it may be helpful to provide some additional rationale for its appearance. If we look at the first law dU=do-dw the term on the left is a function of state, while the two terms on the right are not. For a simple compressible substance, however, we can write the work done in a reversible process as dw= Pdv so that dU=do- Pdv: First law for a simple compressible substance, reversible process Two out of the three terms in this equation are expressed in terms of state variables. It seems plausible that we ought to be able to express the third term using state variables as well, but what are the appropriate variables? If so, the term dg=([I should perhaps be viewed as analogous to dw Pdv where the parenthesis denotes an intensive state variable and the square bracket denotes extensive state variable. The second law tells us that the intensive variable is the temperature, T, and the extensive state variable is the entropy, s The first law for a simple compressible substance in terms of state variables is thus du= Tds-pdv (B.1.1) Because Eq. (B. 1. 1)includes the second law, it is referred to as the combined first and second law Because it is written in terms of state variables, it is true for all processes, not just reversible ones We list below some attributes of entropy a)S is an extensive variable. The entropy per unit mass, or specific entropy, is s 1B-23) There exists a property called entropy, S, which is a thermodynamic property of a system. For a reversible process, changes in this property are given by dS = (dQreversible)/T The entropy change of any system and its surroundings, considered together, is positive and approaches zero for any process which approaches reversibility. ∆Stotal > 0 For an isolated system, i.e., a system that has no interaction with the surroundings, changes in the system have no effect on the surroundings. In this case, we need to consider the system only, and the first and second laws become: ∆E system = 0 ∆S system > 0 For an isolated system the total energy (E = U + Kinetic Energy + Potential Energy + ....) is constant. The entropy can only increase or, in the limit of a reversible process, remain constant. All of these statements are equivalent, but (3) gives a direct, quantitative measure of the departure from reversibility. Entropy is not a familiar concept and it may be helpful to provide some additional rationale for its appearance. If we look at the first law, dU = dQ − dW the term on the left is a function of state, while the two terms on the right are not. For a simple compressible substance, however, we can write the work done in a reversible process as dW = PdV , so that dU = dQ − PdV ; First law for a simple compressible substance, reversible process. Two out of the three terms in this equation are expressed in terms of state variables. It seems plausible that we ought to be able to express the third term using state variables as well, but what are the appropriate variables? If so, the term dQ = ( ) [ ] should perhaps be viewed as analogous to dW = PdV where the parenthesis denotes an intensive state variable and the square bracket denotes an extensive state variable. The second law tells us that the intensive variable is the temperature, T, and the extensive state variable is the entropy, S. The first law for a simple compressible substance in terms of state variables is thus dU = TdS − PdV . (B.1.1) Because Eq. (B.1.1) includes the second law, it is referred to as the combined first and second law. Because it is written in terms of state variables, it is true for all processes, not just reversible ones. We list below some attributes of entropy: a) S is an extensive variable. The entropy per unit mass, or specific entropy, is s. 1B-2