Thermodynamics- validity of change of internal energy equation

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SUMMARY

The equation for internal energy change, \(\Delta U = mC_{v}\Delta T\), is specifically applicable to constant volume processes in thermodynamics, where \(C_{v}\) represents the specific heat at constant volume. This relationship holds true because, under constant volume, no work is done on or by the system, allowing the internal energy change to be directly related to temperature change. However, it is essential to note that while this equation is primarily associated with constant volume, the concept of internal energy change can be applied to other processes, but with different specific heat values, such as \(C_{p}\) for constant pressure processes.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Knowledge of ideal gas laws
  • Familiarity with specific heat capacities, \(C_{v}\) and \(C_{p}\)
  • Basic grasp of thermodynamic processes (constant volume and constant pressure)
NEXT STEPS
  • Study the first law of thermodynamics and its implications on internal energy
  • Learn about the differences between \(C_{v}\) and \(C_{p}\) in various thermodynamic processes
  • Explore the derivation and applications of the ideal gas law
  • Investigate real gas behavior and deviations from ideal gas assumptions
USEFUL FOR

Students preparing for thermodynamics exams, educators teaching thermodynamic principles, and professionals in engineering fields requiring a solid understanding of energy changes in gases.

mjki9ec3
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Just had a thermodynamics exam, and one of the questions was

For an ideal gas, is the relation [tex]\Delta[/tex]U = mC[tex]_{}v[/tex][tex]\Delta[/tex]T restricted to constant volume processes only? Why?

I wrote that it was only valid for constant volume processes, because this is what C[tex]_{}V[/tex] is defined as, however now I'm starting to think that is only true for Q, and that equation is true for any process, not just constant volume.

thanks in advance!
 
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oops, meant to be subscript v's obviously :)
 

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