useful idealizations. For a process to be completely reversible, it is necessary that it be quasi-static and that there be no dissipative influences such as friction and diffusion. The precise(necessary and sufficient) condition to be satisfied if a process is to be reversible is the second part of the Second The criterion as to whether a process is completely reversible must be based on the initial and final states. In the form presented above, the Second Law furnishes a relation between the properti defining the two states, and thereby shows whether a natural process connecting the states is Muddy points What happens when all the energy in the universe is uniformly spread, ie, entropy at a maximum?(MP 1B 1. B3 Combined first and Second law expressions First law. du=dQ-dw- Always true Work and heat exchange in terms of state variables dQ=Tds; dw= Pdv -Only true for reversible processes dU=do-Pdv Simple compressible substance, reversible process du=d@-- Xdr Substance with other work modes(e. g, stress-strain), X is a pressure-like quantity, y is a volume like quantity dU= Tds-dw; Only true for a reversible process First law in terms of state variables dU=Tas-Pav: This is a relation between properties and is always true In terms of specific quantities(per unit mass) du= tds -pdl Combined first and second law(a)or Gibbs equation(a) The combined first and second law expressions are often more usefully written in terms of the enthalpy, or specific enthalpy, h=u+ Pv dh= du t pdv+vd Tds -Pdv+ pdv vdP the first law dh= tds vdP since v=l/p dh= tds t Combined first and second law()or Gibbs equation(b) In terms of enthalpy (rather than specific enthalpy) the relation is dH=TdS vaP 1B-5hu ρ useful idealizations. For a process to be completely reversible, it is necessary that it be quasi-static and that there be no dissipative influences such as friction and diffusion. The precise (necessary and sufficient) condition to be satisfied if a process is to be reversible is the second part of the Second Law. The criterion as to whether a process is completely reversible must be based on the initial and final states. In the form presented above, the Second Law furnishes a relation between the properties defining the two states, and thereby shows whether a natural process connecting the states is possible. Muddy points What happens when all the energy in the universe is uniformly spread, ie, entropy at a maximum? (MP 1B.3) 1.B.3 Combined First and Second Law Expressions First Law: dU = dQ − dW - Always true Work and heat exchange in terms of state variables: dQ = TdS; dW = PdV - Only true for reversible processes. dU = dQ − PdV ; Simple compressible substance, reversible process dU = dQ − PdV − XdY ; Substance with other work modes (e.g., stress-strain), X is a pressure-like quantity, Y is a volume like quantity dU = TdS − dW ; Only true for a reversible process First law in terms of state variables: dU = TdS − PdV ; This is a relation between properties and is always true In terms of specific quantities (per unit mass): du = Tds − Pdv Combined first and second law (a) or Gibbs equation (a) The combined first and second law expressions are often more usefully written in terms of the enthalpy, or specific enthalpy, =+ Pv: dh = du + Pdv + vdP = Tds − Pdv + Pdv + vdP , using the first law. dh = Tds + vdP Or, since v = 1/ ρ dP dh = Tds + . Combined first and second law (b) or Gibbs equation (b) In terms of enthalpy (rather than specific enthalpy) the relation is dH = TdS + VdP . 1B-5