Adiabatic Process, Internal Energy vs. Enthelpy.

AI Thread Summary
The discussion centers on the confusion surrounding the relationships between internal energy (ΔU), enthalpy (ΔH), and work (W) in adiabatic processes. It clarifies that in an adiabatic reversible process, where heat transfer (Q) is zero, work done (W) equals the change in internal energy (ΔU) expressed as nCvΔT. The confusion arises when ΔH is also equated to W as nCpΔT, leading to the realization that these equations apply to different types of systems: closed adiabatic versus open steady-state. The conclusion emphasizes that at constant volume, ΔU relates to heat (qv), while ΔH pertains to heat at constant pressure (qp), reinforcing the relationship Cp - Cv = R. Understanding these distinctions resolves the initial confusion regarding the equality of ΔU and ΔH in different contexts.
Jeremy1789
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I'm struggling to understand a concept which I assume is basic, but I can't seem to fit the pieces together. When speaking about an ideal gas, I understand that

ΔH = ΔU + Δ(PV) = ΔU + RΔT

So far so good. I also understand the relationship:

ΔU = Q + W... (W here is work being done on the system)

In an adiabatic reversible process, Q = 0, which also makes sense. So,

W = ΔU = nCvΔT

Now, where my confusion lies is in the next part. My book works out a problem, and says:

ΔH = W = nCpΔT

How can both ΔU and ΔH equal W? This doesn't make sense to me, unless Δ(PV) from the first equation was 0. I don't see how this could be 0 unless we were talking about an isothermal case. It also doesn't make sense because W can't equal both nCvΔT and nCpΔT simultaneously, since Cp = Cv + R.

Am I missing something?
 
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Never mind. Just answered my own question. The first instance refers to a closed adiabatic system, and the second refers to an open steady-state adiabatic process.
 
How nCvΔT will equal to W.It is the heat absorbed/released at constant volume only(no work is done at constant volume,the expression
Cv).i think instead of work it is heat,ie ΔU=ΔH=qv at constant volume and ΔH=qp at constant pressuer
actually it is the proof for Cp-Cv=R
 
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