Title: Is the enthalpy change in a reversible adiabatic expansion of an ideal gas 0?
Tags: thermodynamics;ideal-gas;reversibility;adiabatic
Question: I would like to know what happens to the enthalpy in a reversible adiabatic expansion for an ideal gas. Will it be greater than or equal to zero?
Comment: Hello. delta U is zero because it is an adiabatic process, but the second part of the expression can either be zero if delta P = 0 or positive if delta P > zero. Will that be correct?

Comment: Thank you Bob, I fully understand it now :)

Comment: Yes, thank you very much

Comment: What do you think? Remember $\Delta H=\Delta U+\Delta (pV)$.

Comment: Sorry Espen. I just now saw your comment. See my answer. Hope it helps.

Comment: Did my answer help?

Comment: So, is my answer acceptable ?

Here is the accepted answer: Will it (the change in enthalpy) be greater than or equal to zero?
It will be less than zero.
The change in enthalpy is
$$\Delta H=\Delta U +\Delta (PV)$$
The first law for a closed system (no mass transfer), any process, is
$$\Delta U=Q-W$$
For any adiabatic process, $Q=0$ and the first law becomes
$$\Delta U=-W$$
so the response to your following comment
delta U is zero because it is an adiabatic process, but the second
part of the expression can either be zero if delta P = 0 or positive
if delta P &gt; zero. Will that be correct?
is $\Delta U$ is not zero for an adiabatic expansion process. It is negative since expansion work $W$ is positive. Since there is no heat transfer to the gas all the expansion work done by the gas is at the expense of its internal energy. Furthermore $\Delta P \ne 0$ and it not greater than zero. It is negative because pressure decreases as the the volume increases in the expansion.
To go on:
For a reversible adiabatic process we have
$$P_{2}V_{2}^{k}=P_{1}V_{1}^{k}$$
$$k=\frac{C_p}{C_v}$$
For an ideal gas, $C_{p}&gt;C_{v}$, therefore $k&gt;1$ making $P_{1}v_{1}&gt;P_{2}v_2$ and $\Delta (Pv)<0$
Since $\Delta U<0$ and $\Delta (Pv)<0$, then $\Delta H<0$
Hope this helps.


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