Q3) A perfectly insulated cylinder fitted with a leakproof frictionless piston with a mass of 30.0 kg and a face area of 400.0 cm? contains 7.0 kg of liquid water and a 3.0-kg bar of aluminum. The aluminum bar has an electrical coil imbedded in it, so that known amounts of heat can be trans- ferred to it. Aluminum has a specific gravity of 2.70 and a specific internal energy given by the formula Û(kJ/kg) be taken to be that of the saturated liquid at that temperature. Negligible heat is transferred to the cylinder wall. Atmospheric pressure is 1.00 atm. The cylinder and its contents are initially at 20°C. 0.94T(°C). The internal energy of liquid water at any temperature may m= 30 kg A-400 cm- H20(v) HOn 7kg H0n ro000 C0000 3 kg Al- Suppose that 3310 kJ is transferred to the bar from the heating coil and the contents of the cylinder are then allowed to equilibrate. (a) Calculate the pressure of the cylinder contents throughout the process. Then determine whether the amount of heat transferred to the system is sufficient to vaporize any of the water. (b) Determine the following quantities: (i) the final system temperature; (ii) the volumes (cm?) of the liquid and vapor phases present at cquilibrium; and (iii) the vertical distance traveled by the piston from the beginning to the end of the process. [Suggestion: Write an energy balance on the complete process, taking the cylinder contents to be the system. Note that the system is closed and that work is done by the system when it moves the piston through a vertical displacement. The magnitude of this work is W = PAV, where P is the constant system pressure and AV is the change in system volume from the initial to the final state.] (c) Calculate an upper limit on the temperature attainable by the aluminum bar during the process, and state the condition that would have to apply for the bar to come close to this tempera- ture.
Q3) A perfectly insulated cylinder fitted with a leakproof frictionless piston with a mass of 30.0 kg and a face area of 400.0 cm? contains 7.0 kg of liquid water and a 3.0-kg bar of aluminum. The aluminum bar has an electrical coil imbedded in it, so that known amounts of heat can be trans- ferred to it. Aluminum has a specific gravity of 2.70 and a specific internal energy given by the formula Û(kJ/kg) be taken to be that of the saturated liquid at that temperature. Negligible heat is transferred to the cylinder wall. Atmospheric pressure is 1.00 atm. The cylinder and its contents are initially at 20°C. 0.94T(°C). The internal energy of liquid water at any temperature may m= 30 kg A-400 cm- H20(v) HOn 7kg H0n ro000 C0000 3 kg Al- Suppose that 3310 kJ is transferred to the bar from the heating coil and the contents of the cylinder are then allowed to equilibrate. (a) Calculate the pressure of the cylinder contents throughout the process. Then determine whether the amount of heat transferred to the system is sufficient to vaporize any of the water. (b) Determine the following quantities: (i) the final system temperature; (ii) the volumes (cm?) of the liquid and vapor phases present at cquilibrium; and (iii) the vertical distance traveled by the piston from the beginning to the end of the process. [Suggestion: Write an energy balance on the complete process, taking the cylinder contents to be the system. Note that the system is closed and that work is done by the system when it moves the piston through a vertical displacement. The magnitude of this work is W = PAV, where P is the constant system pressure and AV is the change in system volume from the initial to the final state.] (c) Calculate an upper limit on the temperature attainable by the aluminum bar during the process, and state the condition that would have to apply for the bar to come close to this tempera- ture.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:Q3)
A perfectly insulated cylinder fitted with a leakproof frictionless piston with a mass of 30.0 kg
and a face area of 400.0 cm? contains 7.0 kg of liquid water and a 3.0-kg bar of aluminum. The
aluminum bar has an electrical coil imbedded in it, so that known amounts of heat can be trans-
ferred to it. Aluminum has a specific gravity of 2.70 and a specific internal energy given by the
formula Ú(kJ/kg)
be taken to be that of the saturated liquid at that temperature. Negligible heat is transferred to
the cylinder wall. Atmospheric pressure is 1.00 atm. The cylinder and its contents are initially at
20°C.
0.94T( C). The internal energy of liquid water at any temperature may
m- 30 kg
A=400 cm-
H2Olv)
7 kg HOn
HOn
Iro000
3 kg Al-
Suppose that 3310 kJ is transferred to the bar from the heating coil and the contents of the
cylinder are then allowed to equilibrate.
(a) Calculate the pressure of the cylinder contents throughout the process. Then determine whether
the amount of heat transferred to the system is sufficient to vaporize any of the water.
(b) Determine the following quantities: (i) the final system temperature; (ii) the volumes (cm) of
the liquid and vapor phases present at equilibrium; and (iii) the vertical distance traveled by the
piston from the beginning to the end of the process. [Suggestion: Write an energy balance on the
complete process, taking the cylinder contents to be the system. Note that the system is closed
and that work is done by the system when it moves the piston through a vertical displacement.
The magnitude of this work is W = PAV, where P is the constant system pressure and AV is
the change in system volume from the initial to the final state.
(c) Calculate an upper limit on the temperature attainable by the aluminum bar during the process,
and state the condition that would have to apply for the bar to come close to this tempera-
ture.
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