Classical thermodynamics problem

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SUMMARY

The discussion centers on a classical thermodynamics problem involving the Second Law of Thermodynamics and the calculation of internal energy and entropy for a solid with a heat capacity proportional to T³. The Second Law is articulated through Kelvin's statement, emphasizing the impossibility of converting heat entirely into work, and Clausius' statement, which prohibits heat transfer from colder to hotter bodies. The user attempts to derive internal energy as CT⁴ but acknowledges this is incorrect, seeking clarification and guidance to efficiently solve the problem for their comprehensive paper.

PREREQUISITES
  • Understanding of the Second Law of Thermodynamics
  • Familiarity with heat capacity concepts
  • Knowledge of internal energy and entropy calculations
  • Basic thermodynamic equations and principles
NEXT STEPS
  • Study the derivation of internal energy from heat capacity in solids
  • Explore the implications of the Second Law of Thermodynamics in various processes
  • Learn about entropy calculations in thermodynamic systems
  • Review classical thermodynamics textbooks for comprehensive problem-solving techniques
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Students in thermodynamics courses, particularly those preparing for comprehensive exams, as well as educators and tutors seeking to clarify concepts related to heat capacity, internal energy, and entropy.

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Homework Statement



(i) State the Second Law of Thermodynamics in one or other of its forms.

(ii) The heat capacity per unit volume of a particular solid at low temperatures is equal to CT3; find expressions for its internal energy and entropy S per unit volume (ignoring the effects of thermal expansion).

Homework Equations



The Attempt at a Solution



(i) Kelvin's statement: No process is possible whose sole effect is complete conversion of heat into work.

Clausius' statement: No process is possible whose sole effect is to transfer heat from a colder to a hotter body.

(ii) Not sure. Any help would be awesome.
 
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Atleast show us the attempt
 
Heat capacity = Internal energy/ Temperature, so Internal energy = CT4. Now, I know that this is wrong, but that's the point of me coming to the forum, so I can get the problem done quickly. Otherwise I can just read the lecture notes and get the problem done in 60 long and boring minutes, which isn't fun becasue I am a third year student and I am studying this for the comprehensive paper and if I take this long to do one problem, then i will take eternity to finish all the first and second year courses and so I might as well pack my bag and run for home.
 

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