dp d +r I P v ds dp dv Integrating between two states I and 2 P2 USing both sides of (B 4.3)as exponents we obtain 22=Py=eAs/cw (B44) Equation(B 4.4)describes a general process. For the specific situation in which As=0,1.e, the entropy is constant, we recover the expression Pv'= constant. It was stated that this expression applied to a reversible, adiabatic process. We now see, through use of the second law, a deeper meaning to the expression, and to the concept of a reversible adiabatic process, in that both are characteristics of a constant entropy, or isentropic, process Muddy points Why do you rewrite the entropy change in terms of Pv?(MP 1B. 4) What is the difference between isentropic and adiabatic?(MP 1B.5) 1. B5 Calculation of entropy Change in Some Basic Processes a) Heat transfer from, or to a heat reservoir a heat reservoir is a constant temperature heat source or sink. Because the temperature is uniform, there is heat transfer across a finite temperature difference and the heat exchange is reversible. From the definition of QH QH entropy(ds=dQ。/T), Q Heat transfer from/to a heat reservoir where Q is the heat into the reservoir(defined here as positive if heat flows into the reservoir) b) Heat transfer between two heat reservoirs Device(block of copper) The entropy changes of the two reservoirs are the sum of the entropy change of each. If the high no change in state temperature reservoir is at TH and the low temperature reservoir is at Ti, the total entropy change is leat transfer between two reservoirs 1B-7    ds = cv dP + dv   + R dv ,  P v v or ds dP dv = + γ . c P v v Integrating between two states 1 and 2 γ ∆s = ln  P2   + γln  v2   = ln P2   v2    . (B.4.3) cv  P1   v1   P1  v1   Using both sides of (B.4.3) as exponents we obtain P vγ 2 s c 22 v = [Pvγ ]1 = e ∆ / . (B.4.4) Pvγ 11 Equation (B.4.4) describes a general process. For the specific situation in which∆s = 0, i.e., the entropy is constant, we recover the expression Pvγ = constant. It was stated that this expression applied to a reversible, adiabatic process. We now see, through use of the second law, a deeper meaning to the expression, and to the concept of a reversible adiabatic process, in that both are characteristics of a constant entropy, or isentropic, process. Muddy points Why do you rewrite the entropy change in terms of Pvγ ? (MP 1B.4) What is the difference between isentropic and adiabatic? (MP 1B.5) 1.B.5 Calculation of Entropy Change in Some Basic Processes a) Heat transfer from, or to, a heat reservoir. A heat reservoir is a constant temperature heat source or sink. Because the temperature is uniform, there is no heat transfer across a finite temperature difference and the heat exchange is reversible. From the definition of entropy (dS = dQrev /T), ∆S = Q , T where Q is the heat into the reservoir (defined here as positive if heat flows into the reservoir) b) Heat transfer between two heat reservoirs The entropy changes of the two reservoirs are the sum of the entropy change of each. If the high temperature reservoir is at TH and the low temperature reservoir is at TL , the total entropy change is TH QH QH Heat transfer from/to a heat reservoir Q TH TL Device (block of copper) no work no change in state Heat transfer between two reservoirs 1B-7