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- 1. Building on our knowledge of gases: 1.6 mole of CO₂ (g) occupies 3.2 L at T = 300 K. If the gas is compressed isothermally at constant external pressure Pext so that the final volume is 1.2 L, calculate the smallest value Pext can have, assuming that CO₂ satisfies the van der Waals equation of state under these conditions. Calculate the work involved using this value of Pext.3. The specific Helmholtz Free energy f is related to the specific internal energy u as: ƒ (T, a) = u — Ts where the "natural variables" of f are temperature and specific volume. a. Expand the differential off in terms of partial derivatives with respect to the natural variables of f b. Using the result from a. and applying the 1st Law of Thermodynamics, what are af T and of la? θα c. From the equality of mixed partial derivatives, show that Op ari la əs θα5. A system consists of a two-phase liquid-vapor mixture of 5 kg of R-134a. One kg is saturated liquid. What is the quality? 6. Given the temperature and specific volume of a two-phase liquid-vapor mixture, how would you determine the specific internal energy? 2
- 4. The first law of thermodynamics states that a. components of a system interact. b. entropy of a closed system always increases. c. closed system always shifts toward disorder or homogeneity. d. Energy is always conserved. 5. According to the second law of thermodynamics, the heat received from a high temperature reservoir by a heat engine operating in a complete cycle a. must be completely converted to work. b. equals the entropy increase. C. converted completely into internal energy. d. cannot be completely converted to work.Q2. What is the total change in entropy when 5.0 kg Of water at 15'℃ is brought into contact with a large heat reservoir at 1000C, after the water reached the temperature of the reservoir - -4186 J/kg,K 18. O5. For a system, the thermodynamic as)vn energy U is defined as a function of S, V, and n which is U(S,V,n) = kn3V 3e3nR %3D where S is the entropy, V is the volume, n is the number of moles, K is the constant, and R is the gas constant. Determine a. Based on the theory in Thermodynamics, (), T = Determine, b. Based on the theory in Thermodynamics, Pressure P = . S,n 5/8 Determine c. Determine ne d. Determine dU in dS, dV and dn