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CHAPTER 7 ENTROPY (some remarks about entropy (SL8) (Carnot cycle (In T-s…

- - - - the area under T-s diagram = integral T.ds = Q (from point 1 to point 2)
        
        :red_flag:the T - dS relation
        
        for a closed stationary system:
        Q - W = Delta U
        or dQ - dW = dU
        or T.dS - P.dv=dU
        
        So T.dS = dU + P.dv :<3:
        another point, h = u + P.v
        or dh = du + d(P.v)
        finally, dh = du + P.dv + v.dP
        Therefore, we have T.ds = dh - v.dP :<3:
        
        we have two equations of ds = 1st and 2nd T.ds equations = Gibbs equation
        (1) ds =
        (2) ds =
        
        valid for all processes because ds does not depend on processes. :red_flag:
        
        Entropy change (ds) of liquids and solids (SL15)
        
        solids and liquids = incompressible substances then cp = cv = c
        
        (1) so entropy change ds for isentropic process of an incompressible substance :question:
        Entropy change ds for ideal gases :question:
        
        note: cv and cp = functions of temperature T
        
        2 ds equations for different volumes or different pressures.
        
        other equations that based on approximate analysis (constant specific heats).
        
        entropy change ds that uses a unit-mole basis (normally used for chemistry).
        
        other equations of ds based on exact analysis (variant specific heats).
    - - the area under P-v diagram = intergral P.dv = W
    - - reminder
        
        energy balance for the steady flow process (according to mass flow rate) E'in = E'out + W'
        or m'. h1= m'.h2 + W'
        or W' = m' (h1- h2) (or W' relates with enthalpy
        
        or W = h1-h2
        
        relation bw efficiency and W (mollier diagram=h-s diagram) :red_flag:
  - - - heat transfer from the hot to cold bodies = irreversible process
        NOTE: the comparison bw the increase and decrease of S in cold and hot bodies, respectively.
- - - - for the reversible cycle :!:
        dS = dQ / T
        or integral of the whole cycle (dQ/T) = 0
        
        what is pass function vs. stat function :question:
        
        SL6
        for a general defintion of Entropy
        
        the first part is not the definition of entropy :!:
        
        the second part = definition of entropy = delta S = S2 - S1 (that related to reversible process)
        
        for the reversible process
        
        for the irreversable processes
        
        S gen always > or = 0
        Notice delta S (of the system) can be negative.