Heat capaticy of isobaric process with real gas

AI Thread Summary
In thermodynamics, the discussion centers on the relationship between isobaric and polytropic processes, particularly when considering non-ideal gases. It is established that an isobaric process can be viewed as a specific case of a polytropic process where the polytropic index n equals zero. The participant struggles with proving this relationship for non-ideal gases, noting that the definition of a polytropic process involves a constant heat capacity, c. The discussion references the equations for heat transfer and changes in enthalpy, highlighting the need for clarity in deriving these relationships. Assistance is sought to further explore the implications of these definitions in the context of non-ideal gases.
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
c \mathrm{d}T = \mathrm{\delta}Q, where c must be constant. For isobaric process we have
c_P = \left(\frac{\mathrm{d}Q}{\mathrm{d}T}\right)_P, 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
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. And know I don't know how to continue. I tried said that
U(T,V(P,T)) and chain rule, but it didn't look better . . .
Thanks for any help . . .
 
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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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