Entropy & Temperature change with applied Magnetic Field

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SUMMARY

The discussion focuses on the relationship between entropy change and temperature change in Gadolinium (Gd) when subjected to a magnetic field of 7.5 Tesla. The initial temperature is specified as 290K, and the mass of Gd is 10kg. The process is adiabatic and assumed to be internally reversible, prompting the inquiry about the applicability of the equation Q = ∫TdS. Participants suggest exploring the relationship between temperature and entropy, particularly through the partial derivative (∂T/∂S)_P to facilitate integration and derive the final temperature.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically adiabatic processes.
  • Familiarity with entropy and its relationship to temperature in thermodynamics.
  • Knowledge of Gadolinium's specific heat capacity and magnetic properties.
  • Proficiency in calculus, particularly integration of differential equations.
NEXT STEPS
  • Research the thermodynamic properties of Gadolinium, focusing on its specific heat capacity.
  • Study the implications of adiabatic processes in thermodynamics.
  • Learn about the mathematical relationship between temperature and entropy, specifically (∂T/∂S)_P.
  • Explore practical applications of magnetic fields on materials and their thermodynamic responses.
USEFUL FOR

Students and professionals in physics and materials science, particularly those studying thermodynamics and the effects of magnetic fields on material properties.

pmccunney
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Can someone please help me on relating an induced magnetic field to entropy change, and ultimately a change in material temperature...

Gadolinium (Gd) undergoes a change in entropy when a field of 7.5 Tesla is applied. This process is adiabatic and the initial temperature is 290K.

Im given the entropy and specific heat data but am confused as to how to relate this entropy change to a final temperature.

Im assuming this is an internally reversible process. If so, does the equation Q= integral of TdS apply?

Any help or point in the right direction would be greatly appreciated...

Also i should mention that the mass of Gd is 10kg

thanks!


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The Attempt at a Solution

 
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pmccunney said:
...am confused as to how to relate this entropy change to a final temperature.

Sounds like a relationship between temperature and entropy, like [itex]\left(\frac{\partial T}{\partial S}\right)_P[/itex], could help, since you could separate the partial differentials and integrate them. Do you know of any physical properties related to this ratio?
 

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