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Thermodynamics Problems: Heat Engine Efficiency & Chemical Equilibrium

Solve thermodynamics problems involving heat engine efficiency, Carnot engine, phase transformations, and chemical equilibrium. Calculate equilibrium temperatures, pressures, and reactant amounts.

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Thermodynamics Problems: Heat Engine Efficiency & Chemical Equilibrium

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  1. # of students Results of Midterm 2 # of students 10 20 30 40 50 60 70 80 90 100 0 points Midterm 1

  2. P 2 T2 1 T1 3 V Problem 1 (heat engine) (20) The heat engine uses an ideal gas as its working substance. 1-2 is an isochoric process, 2-3 – adiabatic, 1-3 – isothermal. T1 and T2 are given. Find Q for each process and the efficiency of the heat engine in terms of T1 and T2 (=1+2/f, CV=(f/2)NkB). (10) Which way of increasing the efficiency of the Carnot heat engine is better – to increase the temperature of the hot reservoir by T (T <<TH, TC) or to decrease the temperature of the cold reservoir by the same T? Explain. 1 – 2 2 – 3 3 – 1

  3. V1, Ti V2, Ti (20) Two insulated tanks with volumes V1and V2are connected by a valve. Each tank contains one mole of the same monatomic van der Waals gas (the constants a and b are known). Initially, when the valve was closed, both gases were at the same temperature Ti. The valve is open and the system reaches its equilibrium state. Find the equilibrium temperature Tf. Is Tf higher or lower than Ti? For which value of V1/V2you expectTfto be equal to Ti? Problem 2 vdW the temperature will decrease if

  4. Problem 3 (phase transformations) (25) The pressure of the saturated water vapor at T = 0.010C is 0.006 bar (these T and P correspond to the triple point of water). The latent heat of the solid-liquid transformation at 0.010C is 335 kJ/kg,the latent heat of the liquid-gas transformation is 2500 kJ/kg. Find the pressure of the saturated water vapor at T = -10C. Along the solid-gas phase equilibrium curve: - the latent heat of sublimation at the triple point - we neglected the volume of solid and expressed the gas volume using the ideal gas law. n – the number of moles in 1 kg.

  5. H2CO3 H2CO3 HCO3-- HCO3-- H+ H+ H (kJ) initial -699.65 1 0 -691.99 0 0 change S (J/K) -x 187.4 + x 91.2 +x 0 final G (kJ) -623.08 1-x -586.77 x 0 x Problem 4 (chem. equilibrium) • (25) Consider the following reaction at T = 298K and P = 1bar: • H2CO3 (aq)  HCO3-- (aq) + H+ (aq) • (a) Using the data in the Table on p.404, calculate G for this reaction, and the equilibrium constant K. (b)If the initial amount of H2CO3 is 1 mole, what will be the amounts of each reactant and product at equilibrium? To obtain the value of G for the reaction, subtract G of the reactants from G of the products: The mass action law: Thus, in equilibrium,

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