Heat capaticy of isobaric process with real gas

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SUMMARY

The discussion centers on the heat capacity of an isobaric process involving real gases, specifically addressing the relationship between isobaric and polytropic processes. The user references the definition of a polytropic process as c dT = δQ, where c remains constant, and highlights the specific heat at constant pressure, c_P, defined as (dQ/dT)_P. The user struggles to derive the relationship for non-ideal gases, attempting to apply the chain rule to express internal energy U as a function of temperature and volume. The conclusion emphasizes the need for clarity in applying thermodynamic principles to real gases.

PREREQUISITES
  • Understanding of thermodynamic processes, specifically isobaric and polytropic processes.
  • Familiarity with the first law of thermodynamics and the concept of heat transfer.
  • Knowledge of specific heat capacities, particularly c_P for isobaric processes.
  • Basic proficiency in calculus, particularly the chain rule for derivatives.
NEXT STEPS
  • Study the derivation of heat capacities for real gases using the ideal gas law as a reference.
  • Explore the application of the chain rule in thermodynamics, particularly in relation to state functions.
  • Investigate the differences between ideal and real gas behavior in thermodynamic processes.
  • Learn about the implications of polytropic processes in practical engineering applications.
USEFUL FOR

Students of thermodynamics, engineers working with gas systems, and researchers focusing on real gas behavior in thermal processes will benefit from this discussion.

lakmus
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Hey,
during last lecture of thermodynamics we did polytropic processes, and with no
discuss teacher said, that isobaric process is in general polytropic. If we had ideal
gas, then it is clear, bud what if the gas isn't ideal?
I tried to proof it, but I stuck and don't know how to continue.
If I write the definition of polytropic process
[itex]c \mathrm{d}T = \mathrm{\delta}Q[/itex], where [itex]c[/itex] must be constant. For isobaric process we have
[itex]c_P = \left(\frac{\mathrm{d}Q}{\mathrm{d}T}\right)_P[/itex], where index right down the derivation notes what state variable is constant. To define the state in thermodynamics, we
need just two state variable, so
[itex]c_P = \left(\frac{\mathrm{d}U(P,T)}{\mathrm{d}T}\right)_P + \left(\frac{P\mathrm{d}V<br /> (P,T)}{\mathrm{d}T}\right)_P[/itex]. And know I don't know how to continue. I tried said that
[itex]U(T,V(P,T))[/itex] and chain rule, but it didn't look better . . .
Thanks for any help . . .
 
Last edited:
Science news on Phys.org
In an isobaric process, $$Q=\Delta H = C_p \Delta T$$. Also, for a polytropic process, $$PV^n=constant$$For an isobaric process, n = 0.
 

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