A thermal cycle has an efficiency equal to 45.0 % of that a Carnot engine that operates between the temperature extremes of the thermal cycle, a low of -70.0 degrees C and a high of 60.0 degrees C. If 9,000.0 J of energy flow into the system at the high temperature in one cycle, how much work is done in the cycle? Tab Your Answer: H Answer Type here to search DIAGG UGLE (O 260LED 4 Jill 3 4 units O 5 99+ O 5099 8 C83°F Mostly sunny la 11:13 8/8/2

A thermal cycle has an efficiency equal to 45.0 % of that a Carnot engine that operates between the temperature extremes of the thermal cycle, a low of -70.0 degrees C and a high of 60.0 degrees C. If 9,000.0 J of energy flow into the system at the high temperature in one cycle, how much work is done in the cycle? Tab Your Answer: H Answer Type here to search DIAGG UGLE (O 260LED 4 Jill 3 4 units O 5 99+ O 5099 8 C83°F Mostly sunny la 11:13 8/8/2

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter4: The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 62P: A Carnot engine operating between heat reservoirs at 500 and 300 K absorbs 1500 J per cycle at the...

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A refrigerator has a coefficient of performance of 3.0. (a) If it requires 200 J of work per cycle, how much heat per cycle does it remove the cold reservoir? (b) How much cycle is discarded to the hot reservoir?
Two hundred grams of water at 0 is brought into contact with a heat reservoir at 80 . After thermal equilibrium is reached, what is the temperature of the water? Of the reservoir? How much heat has been transferred in the process? What is the entropy change of the water? Of the reservoir? What is the entropy change of the universe?
An engine between heat reservoirs at 20 and 200 extracts 1000 J per cycle from the hot reservoir. (a) What is the maximum possible work that engine can do per cycle? (b) For this maximum work, how much heat is exhausted to the cold reservoir per cycle?
The gasoline internal combustion engine operates in a cycle consisting of six parts. Four of these parts involve, among other things, friction, heat exchange through finite temperature differences, and accelerations of the piston; it is irreversible. Nevertheless, it is represented by the ideal reversible Otto cycle, which is illustrated below. The working substance of the cycle is assumed to be air. The six steps of the Otto cycle ale as follows: i. Isobaric intake stroke (OA). A mixture of gasoline and air is drawn into the combustion chamber at atmospheric pressure P0 as the piston expands, increasing the volume of the cylinder from zero to VA . ii. Adiabatic compression stroke (AB). The temperature of the mixture rises as the piston compresses it adiabatically from a volume VA to VB . iii. Ignition at constant volume (BC). The mixture is ignited by a spark. The combustion happens so fast that there is essentially no motion of the piston. During this process, the added heat Q1 causes the pressure to increase from pB to pc at the constant volume VB(=Vc) . iv. Adiabatic expansion (CD). The heated mixture of gasoline and air expands against the piston, increasing the volume from VC to VD . This is called the power stroke, as it is the part of the cycle that delivers most of the power to the crankshaft. v. Constant-volume exhaust (DA). When the exhaust valve opens, some of the combustion products escape. There is almost no movement of the piston during this part of the cycle, so the volume remains constant at VA(=VD) . Most of the available energy is lost here, as represented by the heat exhaust Q2 . vi. Isobaric compression (AO). The exhaust valve remains open, and the compression from VA to zero drives out the remaining combustion products. (a). Using (i)e=W/Q1; (ii)w=Q1Q2; and (iii)Q1=nCv(TCTB),Q2=nCv(TDTA), Show that e=1TDTATCTB. (b). Use the fact that steps (ii) and (iv) are adiabatic to show that e=11r1 where r=VA/VB . The quantity r is called the compression ratio of the engine. (c) In practice, r is kept less than around 7. For larger values, the gasoline-air mixture is compressed to temperatures so high that it explodes before the finely timed spark is delivered. This preignition causes engine knock and loss of power. Show that for r=6 and =1.4 (the value for air), e=0.51 , or an efficiency of 51%. Because of the many irreversible processes, an actual internal combustion engine has an efficiency much less than this ideal value. A typical efficiency for a tuned engine is about 25% to 30%.
Check Your Understanding A Carnot refrigerator operates between two heat reservoirs whose temperatures 0 and 25 . (a) What is the coefficient of performance of the refrigerator? (b) If 200 J of work done on the working substance cycle, how heat per cycle is from cold reservoir? (c) How much heat cycle is discarded to the hot reservoir?
Check Your Understanding A Carnot engine operates between reservoirs at 400 and 30 . (a) What is the efficiency of the engine? (b) If the engine does 5.0 J of work per cycle, how much heat per cycle does it absorb from the high-temperature reservoir? (c) How much heat per cycle does it exhaust to the cold-temperature reservoir? (d) What temperatures at the cold reservoir would give the minimum and maximum efficiency?
Two hundred joules of heat are removed from a heat at a temperature of 200 K. What is the entropy change of the reservoir?
A Carnot engine is used to measure the temperature of a heat reservoir. The engine operates between the heat reservoir and a reservoir consisting of water at its triple point. (a) If 400 J per cycle are removed from the heat reservoir while 200 J per cycle are deposited in the triple-point reservoir, what is the temperature of the heat reservoir? (b) If 400 J per cycle are removed from the triple-point reservoir while 200 J per cycle are deposited in the heat reservoir, what is the temperature of the heat reservoir?
The Carnot cycle is represented by the temperature-entropy diagram shown below. (a) How much heat is absorbed per cycle at the high-temperature reservoir? (b) How much heat is exhausted per cycle at the low-temperature reservoir? (c) How much work is done per cycle by the engine? (d) What is the efficiency of the engine?
Check Your Understanding What is the efficiency of a perfect heat engine? What is the coefficient of performance of a perfect refrigerator?
A Carnot engine operates between 550 and 20 baths and produces 300 kJ of energy in each cycle. Find the change in entropy of the (a) hot bath and (b) cold bath, in each Carnot cycle?
Two hundred grams of water at 0 is brought into contact into thermal equilibrium successively with reservoirs at 20 , 40 , 60 , and 80 . (a) What is the entropy change of the water? (b) Of the reservoir? (c) What is the entropy change of the universe?