In this problem, you will consider an "unusual" solid-state refrigeration device that achieves cooling by varying the magnetization of the working mate- rial (gadolinium sulphate octahydrate) at constant- pressure conditions. By contrast, most refrigeration cycles achieve cooling based on manipulating pres- sures of the working fluid. The device functions roughly as shown at the right wherein a paramag- netic wheel is rotated through different regions: i) a low-temperature region (12) • ii) a low-magnetic field region (23) iii) a high-temperature region (34) iv) a high-magnetic field region (4 → 1) In the figure, the thermodynamic state at the point of entry/exit from each region is shown.

Refrigeration and Air Conditioning Technology (MindTap Course List)
8th Edition
ISBN:9781305578296
Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson
Chapter28: Special Refrigeration Applications
Section: Chapter Questions
Problem 4RQ
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The figure-of-merit indicating the quality of a refrigeration unit is usually the coefficient of performance
 
COP ≡ heat absorbed/net work put in
 
What is the COP for this magnetic refrigeration device?
 
(use wnet = 100 J/mol)
In this problem, you will consider an "unusual"
solid-state refrigeration device that achieves cooling
by varying the magnetization of the working mate-
rial (gadolinium sulphate octahydrate) at constant-
pressure conditions. By contrast, most refrigeration
cycles achieve cooling based on manipulating pres-
sures of the working fluid. The device functions
roughly as shown at the right wherein a paramag-
netic wheel is rotated through different regions:
• i) a low-temperature region (1 → 2)
ii) a low-magnetic field region (2 → 3)
iii) a high-temperature region (3 → 4)
iv) a high-magnetic field region (4 → 1)
In the figure, the thermodynamic state at the point of
entry/exit from each region is shown.
T₁ = 1.1 K
B₁ = 0.9 Tesla
Low temperature "reservoir"
Qc
T₂ = 0.9 K
B₂ = 0.0 Tesla
high
magnetic field
rotating
magnetic
wheel
low
magnetic field
T₁ = 9.5 K
B₁ = 6.4 Tesla
QH
high temperature "reservoir"
T3 = 8.0 K
B3 = 1.6 Tesla
Transcribed Image Text:In this problem, you will consider an "unusual" solid-state refrigeration device that achieves cooling by varying the magnetization of the working mate- rial (gadolinium sulphate octahydrate) at constant- pressure conditions. By contrast, most refrigeration cycles achieve cooling based on manipulating pres- sures of the working fluid. The device functions roughly as shown at the right wherein a paramag- netic wheel is rotated through different regions: • i) a low-temperature region (1 → 2) ii) a low-magnetic field region (2 → 3) iii) a high-temperature region (3 → 4) iv) a high-magnetic field region (4 → 1) In the figure, the thermodynamic state at the point of entry/exit from each region is shown. T₁ = 1.1 K B₁ = 0.9 Tesla Low temperature "reservoir" Qc T₂ = 0.9 K B₂ = 0.0 Tesla high magnetic field rotating magnetic wheel low magnetic field T₁ = 9.5 K B₁ = 6.4 Tesla QH high temperature "reservoir" T3 = 8.0 K B3 = 1.6 Tesla
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