Assignment #14

Sections 19-1 & 19-2

Due: Tue. Feb. 12

14. What is the final temperature of the following if 215 kJ {834 cal} of heat energy is added to each:

(A) A 1.78 kilograms {23.0 grams} of water at 56.0 ^oC {4.60 ^oC}.
(B) A 150 kilograms {370 grams} of copper at -22.0 ^oC.
(C) A 13.5 kg {120 grams} of copper and 2.60 kg {89.0 grams} of water in thermal contact with each other, both initially at 14.6 ^oC {0.00 ^oC}.
(D) What fraction of the 215 kJ {834 cal} of energy added goes into the water {copper} in the last question (C) ?
BONUS:
(E) A 760 g {6.70 g} block of ice at -5.00 ^oC.

{ANS:} #14

(A) 40.9oC

(B) 2.39oC

(C) 8.33oC

(D) 11.1%

(E) 42.0oC

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Assignment #15

Sections 19-1 & 19-2

Due: Wed. Feb. 13

15-1. A 500 Watt {750 W} electrical heater is placed in an insulated container into which 350 g {14.0 g} of ice at -13.0 ^oC and turn on. If no heat is exchanged with the environment,

(A) how long will it take to just melt the ice so that there is only water at 0 ^oC in the container ?
(B) how long will it take to evaporate the water starting from 0 ^oC ? }

15-2. An insulated container contain 3.90 kg {1.25 kg} of water at 20.0 ^oC. What is the final temperature if the following is added to the container ?

(A) 1.25 kg of water at 97.0 ^oC {80.0 ^oC}.
(B) 482 grams {780 g} of Aluminum at 112 ^oC.
BONUS:
(C) 28.0 grams of steam at 100 ^oC {210 g of ice at 0 ^oC}.

{ANS:} #15

15-1. (A) 6.78 s (B) 50.0 s

15-2. (A) 50.0oC (B) 30.9oC (C) 5.66oC

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Assignment #16

Sections 19-3 & 19-5

Due: Fri. Feb. 15

16. A cylinder fitted with a frictionless piston has an initial volume of 2.20 liters {3.30 l}. The cylinder's chamber contains an ideal gas ( c_p = 20.8 J/mole/ ⁰C) under a pressure of 3.22x10 ⁵ Pa at 28.0 ^oC initially. The Gas is allowed to expand to a final volume of 7.90 liters. Sketch the P-versus-V diagram for each of the following processes and determine (a) work done by the gas, (b) the final temperature, and (c) the final pressure of the gas if :

(A) the gas expands against a constant pressure of 3.22x10 ⁵ Pa.
(B) the gas expands slowly so that its temperature remains constant during the expansion.
(C) the gas expands in such a way that P = a(V - V _b) during the process, where a = 1.80x10 ⁸ N/m⁵ and V_b = .411 liters {1.51 l}

{ANS:} #16

(A) 1.48 kJ, 721 K, 322 kPa

(B) 928 J, 301 K, 135 kPa

(C) 3.39 kJ, 2580 K, 1.15 MPa

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Assignment #17

Sections 19-5 & 19-6

Due: Mon. Feb. 19

17. A cylinder with an initial volume of 2.20 liters {3.30 l} is fitted with a frictionless piston. The cylinder's chamber contains an ideal gas ( c_p = 20.8 J/mole/ ^oC) under a pressure of 3.22x10 ⁵ Pa at 28.0 ^oC initially. Sketch the P-versus-V diagram for the gas when 910 cal {540 cal} of heat is added to the gas in the cylinder and

(A) the piston is clamped down so that the volume of the gas remains constant while the heat is added. Determine the work done by the gas, the change in internal energy, the final temperature and pressure.
(B) the piston is allowed to expand against a constant pressure of 322 kPa while the heat is added. Determine the work done by the gas, the change in internal energy, the final temperature and volume.
(C) the gas expands in such a way that P = aV ² during the process and the final pressure is 801.7 kPa {537.8 kPa}. Determine the constant a, the final volume, the work done by the gas, and the change in internal energy.
BONUS:
(D) the gas in cylinder is allowed to expand in such way that its temperature constant while the heat is added. Determine the work done by the gas, the change in internal energy, the final volume and pressure.

{ANS:} #17	(A) W = 0, DU = 2.26 kJ, Tf = 727 K, Pf = 777 kPa
	(B) W = 903 J, DU = 1.36 kJ, Tf = 557 K, Vf = 6.01 l
	(C) a = 2.96x10 10 N/m 8, Vf = 4.26 l, W = 410 J, DU = 1.85 kJ
	(D) W = 2.26 kJ, DU = 0, Vf = 27.7 l, Pf = 38.4 kPa

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Assignment #18

Section 19-9

Due: Wed. Feb. 20

18. A heat engine uses 1.30 g of air ( C_p = 1003.5 J/kg/ ^oC, C_v = 716.5 J/kg/ ^oC, M = 28.97 gram/mole) a working substance. Initially, call this point A, the air starts out compressed to a volume of 160 cm ³ {240 cc} and a temperature of 680 K {795 K}. The air is then allowed to rapidly expand to a pressure of 150 kPa {201 kPa}, call this point B, in such a way that no heat is lost from working substance while the engine does external work. The air is then compressed and cooled at a constant pressure until its volume is equal to its starting volume of 160 cm ³ {240 cc}, call this point C. During the final portion of the cycle, from point C back to A, the gas is heated while the volume remains fixed until the gas is back to its starting pressure, volume, and temperature.

(A) Sketch the process on a P-versus-V diagram and determine the pressure, volume, and temperature at points A, B, and C.
(B) Calculate the external work done by the heat engine, and the work done in compressing the gas back to its starting state after it has accomplished external work.
(C) Calculate the heat lost by the air during the constant pressure compression, and the heat added during the constant volume heating portion of the cycle.
(D) Calculate the change in internal energy of the air during each portion of the cycle, and the net change in internal energy during each complete cycle.
(E) Show that the net work done on and by the air is equal to the net heat gained by the air during a each complete cycle.

{ANS:} #18	(A) PA = 1.24 MPa, T A = 795 K, V A = 240 cc , PB = 201 kPa , T B = 473 K, V B = 878 cc , PC = 201 kPa , T C = 129 K, V C = 240 cc
	(B) Wout = 300 J, Win = -128 J
	(C) Qout = -448 J, Qin = 620 J
	(D) DUAB = -300 J, DUBC = -320 J, DUCA = +620 J, DUnet = 0.00 J
	(E) Wnet = 172 J, Qnet = 172 J

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