4. Consider a heat engine comprising two isochores and two isobars, as in the diagram below. Suppose vertices 2 and 4 are connected by an isotherm of temperature To, while the temperatures at vertices 1 and 3 are T₁ and T3, respectively. Compute the efficiency of this cycle. To 2 T₁ 1 3 T3 4 To a
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- The figure represents a Carnot engine that works between temperatures T₁ = 410 K and T₂ = 150 K and drives a Carnot refrigerator that works between temperatures T3 = 345 K and T4 =245 K. What is the ratio of Q3/Q1? and Number i T₁ H Refrigerator To Engine Unitsin a single cycle, a heat engine extracts 8.00 kcal of heat from a hot reservoir and exhausts 5.00 kcal of heat int a cold reservoir. What is the efficiency of this engine? a. 47.5% b. 37.5% c. 67.5% d. 57.5% e. 77.5%Question B2i. Give an equation for the infinitesimal change in entropy, ??, of a system in terms of the heat transfer ??? and the temperature ? at which the heat transfer occurs. Explain the sign convention. ii. A litre of water at 20 °C is placed in a fridge at 5 °C. Calculate the change in entropy of the water, including the sign, once all the water has come into thermal equilibrium. iii. Calculate the change in entropy of the fridge from part ii, including the sign. iv. Demonstrate that the Second Law has been obeyed in the process described in ii and iii.
- B2Figure beside shows a p-V graph for a series of p(N m³), thermodynamic processes, ABC. In process AB and BC, 160 J and 600 J are added to the system respectively. Calculate the change of the internal energy during the process ABC. 9. B 8 x 10* [440 J] 2 x 10 A 2 x 10 6x 10 V(m³)How much heat energy is needed to change the entropy of a macrostate from 10.00 J/K to 10.01 J/K in a quasi-static process at a temperature of 30 K? Express your answer with the appropriate units. Q30: = Submit Part B Q300= Submit Part C 0 ¤-| |μÅ How much heat energy is needed to change the entropy of a macrostate from 10.00 J/K to 10.01 J/K in a quasi-static process at a temperature of 300 K? Express your answer with the appropriate units. Q3000 Value = Request Answer 0 Value Request Answer Units How much heat energy is needed to change the entropy of a macrostate from 10.00 J/K to 10.01 J/K in a quasi-static process at a temperature of 3000 K? Express your answer with the appropriate units. 0 PHμÅ Value 2) ? Units Units
- 5. A Carnot refrigerator runs between a cold reservoir at temperature Tc and a hot reservoir at temperature Tµ. You want to increase its coefficient of performance. Of the following, which change results in the greatest increase in the coefficient? The value of AT is the same for all changes. a. Raise the temperature of the hot reservoir by AT b. Raise the temperature of the cold reservoir by AT c. Lower the temperature of the hot reservoir by AT d. Lower the temperature of the cold reservoir by ATIdentify the processes in the cycle. Þ 1. Path AB = The temperature in (1) is 350 K, the work done in (2) is 7.0 J with no heat applied/released, and the pressure in (3) is 3 atm. The change in internal energy in (5) is 12.0 J (with no heat applied or released). 2. Path BC = 3. Path CD= 4. Path DE= D 5. Path EA = V 6. What is the change in internal energy of the (ideal) gas along path (3) in joules? *Indicate whether the process is compression or expansion, e.g. isobaric expansion, etc.Tq
- Consider a heat engine transferring energy from a warm region (Tw) to a cool region (Tc) . Which combination of temperatures will result in the highest efficiency? a. Tw = 500 K, Tc = 400 K b. Tw = 500 K, Tc = 300 K c. Tw = 500 K, Tc = 450 K d. Tw = 300 K, Tc = 300 K6. A heat engine consists of the cycle p shown for 3 moles of an ideal 2p monatomic gas. It starts at point 1 with pressure p and volume V; it goes via an isochoric (constant 1 volume) process from point 1 to 3 point 2 until the pressure doubles; it then goes from point 2 to point 3 via an adiabatic process; finally it goes V from point 3 to point 1 via an isothermal process. А. I What is the volume of the gas at point 3? Express your answer in terms of V (the volume of the gas at point 1). В. What are W12, W23, and W31? Express your answer in terms of p, V. 2.A heat engine provides a net power output of 14 kW and has an efficiency of 23 %. The engine rejects 1200 J of energy per cycle to a low temperature reservoir. a)Determine the amount of heat delivered to the engine from the high temperature reservoir per second. Your answer should be in units of Watts. b)Determine the required number of cycles per minute executed.