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Enthalpy of condensation

Physics Asked by Azwar Abdulsalam on February 26, 2021

suppose we have one mole of an ideal gas undergoing a phase change at constant temperature. we know that enthalpy change is given by the formula $ncdot Cpcdotdelta(T)$. since there is no temperature change therefore enthalpy change should be zero,

  • however it is not?where am i going wrong?

4 Answers

During a phase change, the intermolecular forces change. This is because the average separation of the molecules changes, changing the average potential energy. Since potential energy is a component of internal energy and it requires work or heat to change the internal energy, it follows that an enthalpy change must occur during a phase change.

Also for a phase change, the formula nCpT=Q no longer applies. The enthalpy change is given by mass (m) and latent heat of vaporisation (L)

Q=mL

Answered by Jaywalker on February 26, 2021

Where am I going wrong?

There is no liquid or solid that behaves like an ideal gas. So, there is no phase changing for any ideal gas. Ideal gas isn't a specific gas like oxygen, hydrogen, etc. It is an ideal behavior assumption. Liquid oxygen (for instance) isn't an ideal gas and so we cannot use the formula $mathrm dh=C_pmathrm dT$ because this formula has been obtained by ideal gas behavior assumption.

Answered by lucas on February 26, 2021

Enthalpy change of an ideal gas is given by the formula $dH = n c_p dT$ when it undergoes a change in temperature $dT$.

This formula is no longer valid when you undergo a phase transition : for a given quantity of water at a given temperature to vaporize requires a huge amount of enthalpy. See for example this wikipedia article.

Also, as it was noted in lucas' answer, an ideal gas cannot undergo a phase transition as you need molecular interaction to trigger it, which is absent in the ideal gas model.

Answered by Dimitri on February 26, 2021

By definition $c_p = {(partial h/partial T)}_P$ is valid only for a "homogeneous phase of a substance of constant composition,...no change of phase..." [Sonntag and Van Wylen, Thermodynamics] The same caveat applies to $c_V = {(partial u/partial T)}_V$. So the concept of specific heat does not apply to a change in phase.

Hope this helps.

Answered by John Darby on February 26, 2021

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