19. An engineer claims to have invented a new type of heat engine that takes in 167 cal of heat per cycle at 365 oC {310 oC}, accomplishes 200 J {500 J} of work per cycle, and eject 128 cal {47.5 cal} of heat into the environment at 20.0 oC.
Assignment #19
Sections 20-1 & 20-4
Due: Tue. Feb. 26
(A) Does his invention violate the first law of thermodynamics ? Prove your answer (to the accuracy of three significant figures) by verifying that the energy is conserved or not conserved.
(B) What thermal efficiency would he claim for his heat engine if it took in 167 cal and put out 200 J {500 J} of work ?
(C) Using the conservation of energy, what would be the thermal efficiency of this heat engine calculated on the basis that it did take in 167 cal of heat and exhaust 128 cal {47.5 cal} ?
(D) If this heat engine did take in 167 cal of heat and put out 200 J {500 J} of work, would the engineer's invention violate the second law of thermodynamics ? Prove your answer by calculating the Carnot efficient for this engine.
BONUS:
(E) What minimum value would the upper temperature have to have in order to take in 167 cal of heat and put out 200 J {500 J} of work if it exhausts its waste heat into the environment at 20.0 oC, i.e., if the engine operated at the maximum possible efficiency, what would the upper temperature T h have to be ?
| {ANS:} #19 | (A) No, energy is conserved | (B) 71.5% | (C) 71.5 % |
| (D) Yes, it violates the 2nd law, emax = 49.7% < 71.5% | (E) 1030 K |
20-1. A refrigerator operates at a low temperature of -5.00 oC {-10.0 oC}, and exhausts heat into the air at 21.0 oC. The motor of the refrigerator produces 3/4 horsepower of useful work to operate the refrigeration cycle.
Assignment #20
Sections 20-2 &20-5
Due: Wed. Feb. 27
(A) What is the maximum coefficient of performance of this refrigerator ? }
(B) How much heat does this refrigerator exhaust into the environment each second if it operates at 43.0% of its maximum coefficient of performance ? }
(C) If this refrigerator operated at 43.0% of its maximum efficiency, how long would it take to cool and freeze 4.20 kg of water at 18.0 oC to ice at 0 oC when placed in the refrigerator ?
20-2. A heat pump with a coefficient of performance of 5.70 {8.40} delivers 7300 BTU/hr {4800 BTU/hr} from outdoor air at -12.0 oC {-15.0 oC} to the air inside a house at 22.0 oC.
(A) How much electrical energy does the heat pump use each second ?
(B) Does this heat pump violate the second law of thermodynamics ?
| {ANS:} #20 |
20-1. (A) 8.49 (B) 2.60 kW (C)14.0 min |
20-2. (A) 167 W (B) Yes, it does violate the 2nd law, COPmax = 7.97 < 8.40 |
21-1. Calculate the change in entropy of 13.5 grams {7.62 kg} of water when
Assignment #21
Section 20-7
Due: Fri. March 1
(A) the water initially at 0.00 oC is frozen to ice at 0.00 oC.
(B) the water initially at 100 oC is vaporized to steam at 100 oC.
(C) the water initially at 100 oC is cooled to 0.00 oC
21-2. If 685 grams {1.90 kg} of ice at 0.00 oC is mixed with 2.57 kg of water at 13.0 o {21.0 oC} calculate the change in entropy of
(A) the ice that does not melt.
(B) the ice that melts.
(C) the water.
(D) the universe.
| {ANS:} #21 |
21-1. (A) -9.30 kJ/K (B) +46.1 kJ/K (C) -9.95 kJ/K |
22-2. |
Assignment #22
Section 20-7
Due: Mon. March 4
|
22-1. The Stirling engine cycle consist of:
A -> B: an isothermal compression stage where work is done on the working substance and heat is removed while it is compress to point B. B -> C: a constant volume heating stage were the working substance is heated to its highest temperature and pressure. C -> D: an isothermal expansion stage where the working substance does work while it absorbs heat at the same time to maintain a constant temperature. D -> A: a constant volume cooling stage were the working substance is returned to its original state. |
The heat lost during the BC cooling stage is used to heat the working substance during the DA stage. Since they are equal in magnitude, the heat loss and gain can be ignored during these two stages. |
 |
(A) Calculate the change in entropy for each stage and the total change in entropy of the working substance for 4.30 moles {5.80 moles} an ideal gas ( cp = 20.8 J/mole/K) operating between T h = 280 oC {350 oC} and T l = 62.0 oC. (B) Determine the net work done by such an engine. |
BONUS:
(E) Prove symbolically that the thermal efficiency is equal to the Carnot efficiency, i.e., show that e th = e max, for any values of pressure and volume.
| {ANS:} #22 | (A) DSAB = -70.7 J/K, DSBC = 44.7 J/K, DSCD = 70.7 J/K, DSDA = -44.7 J/K, DStot = 0 |
| (B) Wnet = WAB + WCD =-23.7 kJ+44.1 kJ = 20.4 kJ | |
| (C) Qin = QCD = 44.1 kJ, Qout = QAB = -23.7 kJ | |
| (D) eth = 46.2%, emax = 46.2% | |
| (E) ? |
| Assignment #23 | Section 20-8 | Due: Tue. March 5 |
(B) If the heat engine is reversible, what must be the change in entropy of the ice-water in the vat ? (C) If the heat engine is reversible, how much heat will be dumped into the vat of ice and water ? (D) What is the total amount of work that this heat engine can accomplish ? (E) Show that the thermal efficiency of this reversible heat engine is less than the maximum possible thermal efficiency of a Carnot heat engine operating between the same two temperatures. |
 |
| {ANS:} #23 | (A) DSCu = -4.78 Kcal/K or -20.0 KJ/K | (B) ? | (C) 1.31 Mcal or 5.47 MJ |
| (D) W = 4.80 MJ | (E) eth = 46.7% < emax = 68.4% |
START for CHAPTER 21
24-1. At 22.0 oC an aluminum {steel use a = 12x10 -6 1/ 0C} bar and a copper bar have the same length of 12.2 m {240 cm}. The bars are placed on top of each other and one of their ends are welded together.
Assignment #24
Section 21-1
Due: Wed. March 6
(A) When the temperature is raised to 280 oC {330 oC} which bar is the longest, and what is the separation between their free ends ?
(B) When the temperature is lowered to -180 oC {-130 oC} which bar is the longest, and what is the separation between their free ends ?
BONUS:
(C) At what two temperatures will the separation between the two free end be exactly one mm {one half of a mm} ?
24-2. What is the volume of 10.0 kg of mercury at 98.5 oC {76.3 oC} if mercury has a density of 1,365 kg/m 3 at 20.0 oC ?
24-3. A piece of copper tubing used in plumbing has a inner radius of 1.25 cm at 20.0 oC. When hot water at 71.6 oC {83.0 oC} is flowing through the tube, by how much will the cross-sectional area change ?
| {ANS:} #24 |
24-1. (A) copper, 3.70 mm (B) steel, 1.82 mm (C) -19.7oC, 63.7 oC |
24-2. 7.40 liters |
24-3. 1.05 mm 2 |
25-1. A 1.50 m by 2.00 m glass window has a thickness of 3.00 mm {5.00 mm} and thermal conductivity k = .750 W/m- oC.
Assignment #25
Section 21-4
Due: Fri. March 8
(A) How much heat flows through this window when the indoor temperature is maintained at 65.0 o F {72.0 oF} while the outdoor temperature is -12.0 oF ?
(B) If the window is covered over with 1.50 cm {.780 cm} thick piece of plywood that has a k = .120 W/m- oC, how much heat flows through the covered window when the indoor temperature is 65.0 o F {72.0 oF} while the outdoor temperature is -12.0 oF ?
BONUS:
(C) What is the temperature between the plywood and the glass under these conditions if the plywood is placed on the out side of the window ?
25-2. One end of a 1.45 m {75.0 cm} long, flexible copper rod (radius = 1.32 cm) is placed in boiling water at 100 oC and the other end in ice-water mixture at 0.00 oC. If the copper rod is well insulated along its length so that no heat is lost out the sides of the rod,
(A) what is the heat flow in watts through the copper rod ?
(B) how long would it take for enough heat to flow through the copper rod to melt 76.0 grams of ice in the ice-water mixture ? (See section 18.4 for heat to melt ice.)
| {ANS:} #25 |
25-1. (A) 21.0 kW (B) 1.95 kW (C) 64.2oF |
25-2. (A) 29.2 W (B) 868 sec |