Proof Ideal Gas: (dU/dV)T=0 & (dH/dP)T=0

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SUMMARY

The discussion focuses on proving the equations (dU/dV)T=0 and (dH/dP)T=0 for an ideal gas. It is established that the internal energy (U) of an ideal gas is solely a function of temperature (T), leading to the conclusion that the change in internal energy with respect to volume at constant temperature is zero. Similarly, the enthalpy (H), defined as H = U + PV, also depends only on temperature when using the ideal gas equation, resulting in (dH/dP)T=0. The moderator's warning indicates that the discussion strayed from academic norms.

PREREQUISITES
  • Understanding of thermodynamic concepts such as internal energy and enthalpy.
  • Familiarity with the ideal gas law and its implications.
  • Knowledge of partial derivatives in thermodynamics.
  • Basic principles of constant temperature processes.
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  • Study the derivation of the ideal gas law and its applications.
  • Learn about the relationship between internal energy and temperature for different substances.
  • Explore the concept of enthalpy and its significance in thermodynamic processes.
  • Investigate the implications of constant temperature processes in thermodynamics.
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This discussion is beneficial for students and professionals in thermodynamics, particularly those studying ideal gas behavior, internal energy, and enthalpy relationships in physical chemistry or engineering contexts.

Hong1111
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How to prove that

(a)(dU/dV)T=0
(b)(dH/dP)T=0

for an ideal gas.

Where U is internal energy per unit mass, V is volume, T is temperature (which is held constant for above 2 question), H is the enthalpy per unit mass, and P is the pressure.

I found this in a thermodynamics textbook. This is not a homework question. I just want to know how does this apply to ideal gas and how to derive the both equations. And in the end, I got warning from moderator.

Thanks.
 
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For an ideal gas you should find that the internal energy is only a function of T, hence dU/dV is definitely zero.

Same applies for the enthalpy, define H = U + PV, use the ideal gas equation to substitute for PV and you'll see that H is only a function of T as well, so dH/dP is zero.

I don't see the point of those equations though =/
 

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