- Part A A real heat engine working between heat reservoirs at 940 K and 570 K produces 680 J of work per cycle for a heat input of 2700 J. Compare the efficiency of this real engine to that of an ideal (Camot) engine Express your answer using two significant figures. [5] ΑΣΦΑ ? Submit Request Answer Part B Calculate the total entropy change of the universe per cycle of the real engine. Express your answer to two significant figures and include the appropriate units. μÁ 1 ? AS = Value Units Submit Request Answer Part C Calculate the total entropy change of the universe per cycle if the engine is ideal (Carnot). Express your answer to two significant figures and include the appropriate units. μA BMC ? AS = Value Units Submit Request Answer

- Part A A real heat engine working between heat reservoirs at 940 K and 570 K produces 680 J of work per cycle for a heat input of 2700 J. Compare the efficiency of this real engine to that of an ideal (Camot) engine Express your answer using two significant figures. [5] ΑΣΦΑ ? Submit Request Answer Part B Calculate the total entropy change of the universe per cycle of the real engine. Express your answer to two significant figures and include the appropriate units. μÁ 1 ? AS = Value Units Submit Request Answer Part C Calculate the total entropy change of the universe per cycle if the engine is ideal (Carnot). Express your answer to two significant figures and include the appropriate units. μA BMC ? AS = Value Units Submit Request Answer

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter4: The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 41P: A Carnot engine is used to measure the temperature of a heat reservoir. The engine operates between...

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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?
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%.
Consider an ideal gas Joule cycle, also called the Brayton cycle, shown below. Find the formula for efficiency of the engine using this cycle in terms of P1 , P2 and .
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?
Two hundred joules of heat are removed from a heat at a temperature of 200 K. What is the entropy change of the reservoir?
Check Your Understanding A 50-g copper piece at a temperature of 20 is placed into a large insulated vat of water in 100 . (a) What is the entropy change of the copper piece when it reaches thermal equilibrium with the water? (b) What is the entropy change of the water? (c) What is the entropy change of the universe?
An ideal gas expands isothermally along AB and does 700 J of work (see below). (a) How much heat does the gas exchange along AB? (b) The gas then expands adiabatically along BC and does 400 J of work. When the gas returns to A along CA, it exhausts 100 J of heat to its surroundings. How much work is done on the gas along this path?
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?
A 0.50-kg piece of aluminum at 250 is dropped into 1.0 kg of water at 20 . After equilibrium is reached, what is the net entropy change of the system?
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?
A diatomic ideal gas is brought from an initial equilibrium state at p1=0.50 atm and T1=300K to a final stage with p2=0.20 atm and T1=500K. Use the results of the previous problem to determine the entropy change per mole of the gas.
(a) A 5.0-kg rock at a temperature of 20 is dropped into a shallow lake also at 20 from a height of 1.0103 m. What is the resulting change in entropy of the universe? (b) If the temperature of the lock is 100 when it is dropped, what is the change of entropy of the universe? Assume that air friction is negligible (not a good assumption) and that c=860 J/kg K is the specific heat of the rock.