Question

02) Consider a hydrostatic system represented by the thermodynamic variables volume V, pressure P and temperature T. a) Consider entropy S = S(T, V) and derive the equation TdS. Tas = Cvat +T (1) dV. V Show that this equation can be written as follows BT TdS = CydT + PDV where Cv is the thermal capacity at constant volume, B is the isobaric expansiveness and K is isothermal compressibility: b) Consider a gas described by the equation of state p(V - b) = nRTe-aT where n is the number of moles, R is the molar constant of the gases and a and b are constant, and show that Cp – Cv = nR(1 – aT)? exp(-al). c) Consider a gas whose free Helmholtz energy is given by F = F(T,V) = -n RT In -b(T)V, C.) e-- where n is the number of moles, R is the molar constant of the gases and a and Vo are onstant. Determine the equation of state, the entropy. S = S(T, V) of the system and the thermal capacity at constant volume Cv. The system described by the energy above can be observed at temperature T = 0? Justify your answer. d) A hydrostatic system undergoes a phase transition from first order to temperature To = 300 K and pressure Po = 1 x 106 Pa In this case, it is verified that the variation of the specific volume of the system Av = 2 x 10-m/Kg and the variation of the enthalpy specific Ah = 60 KJ/Kg. Determine the variation of the specific entropy for this phase transition. Determine the temperature T1 of the transition if it occurs at a pressure P.1.-1.x 105 Pa... Indicate the hypothesis considered in this second case.

Answer 1

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page-2 → 3 f), - (3), + 6), T(**)-7(3), - T (55) ( T (2) Core T2 ( 3 Op -(v2 JT Ir from read well relation, (09), - ()) No, pz C nRenat (V-b -nRaerds (V-5) nRe-dy P nRideat Vb Porno 2 - Cp-cu 2 ñ Rare-205 Tx P (vb) Tx n Ram e-207 nRendt MR (To). e-&T.

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