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

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For an ideal gas, the internal energy (U) is solely a function of temperature (T), leading to the conclusion that (dU/dV)T=0. Similarly, enthalpy (H) can be expressed as H = U + PV, and using the ideal gas equation reveals that H is also a function of T, resulting in (dH/dP)T=0. The discussion highlights the derivation of these equations, emphasizing their dependence on temperature rather than volume or pressure. Despite the mathematical proof, some participants question the practical significance of these equations in thermodynamics. Understanding these principles is essential for grasping the behavior of ideal gases.
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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