# Latent heat of vaporization/evaporation

It's the amount of heat required for liquid ---> gas phase change of a substance at it's Boiling point.

But my question is, does providing energy equivalent to latent heat of vaporization to a liquid at a temperature below it's Boiling point (if you need, also assume above it's Freezing point) 'Evaporate' it?

eg. When water is kept inside a clay pot out in the Sun, we know a very small amount of water somehow seeps out through it's pores and 'evaporates' (if not vaporizes). Obviously the temperatures aren't even close to 373K(boiling point of water), but the water is spontaneously turning into steam. Because it's not boiling, but is simply evaporating which can take place any where below it's boiling point. But the point here is, 'how much' of the energy from the rest of water-pot system is entrapped in order to convert into a form that has got more energy than its predecessor. Is it equivalent to only the amount of latent heat of vaporization or is it plus the amount of energy required to raise it's temperature upto it's boiling point.

• Hint question: What is the relation of the latent heat of evaporation ( J/kg ) at 2 different temperatures and respective specific heats ( J/kg/K) of water and water vapour ? Can the total energy change going through the whole closed cycle ( both temperatures and phases ) be nonzero ? Aug 17 '20 at 14:26
• @Poutnik I did think upon the hints but I didn't get you. Like, the first relationship you are talking about is something I didn't know, and even after acknowledging that I didn't have access to the 'papers' stating the relationship. Second, I didn't get which cycle you wanted to refer to. Kindly help. Aug 18 '20 at 1:53
• @Poutnik You are asking? It's only =latent heat. But I don't have an intuition or even an understanding of it! Aug 18 '20 at 4:34

Latent heat of vaporization/evaporation: It's the amount of heat required for liquid ---> gas phase change of a substance at it's Boiling point.

Not exactly. It's the amount of heat required for liquid ---> gas phase change of a substance at the particular temperature, there is usually and implicitly the substance boiling point. But generally, it is defined for any temperature.

Is it equivalent to only the amount of latent heat of vaporization or is it plus the amount of energy required to raise it's temperature upto it's boiling point.?

Neither, neither. It is between these 2 values.

The latent heat of water evaporation at temperature $$T_2 \lt T_1$$ (let we take $$T_1$$ as the boiling point ) is equal to the latent heat of vaporization at temperature $$T_1$$ plus the heat required to warm up water from $$T_2$$ to $$T_1$$ minus the heat released to cool down vapour from $$T_1$$ to $$T_2$$.

$$\Delta H_{\mathrm{evap},T_2} = \Delta H_{\mathrm{evap},T_1} + C_\mathrm{p,water}\cdot (T_1 - T_2) + C_\mathrm{p,vapour}\cdot (T_2 - T_1)$$

where $$\Delta H$$ are molar latent evaporation heats at constant pressure ( called molar enthalpies of evaporation) at respective temperatures,
$$C_\mathrm{p}$$ are respecive molar heat capacities of water and vapour ( for simplicity considered constant to avoid integrals).

It is application of the Hess' law, which is application of the energy conservation law. It says the energy change depends only on the initial and final state, not on the way how is the final state reached. If it were not so, we could easily construct perpetuum mobile by switching between 2 states by 2 different ways.

So getting A->B directly, or A->C->D->B is equivalent, where

• A is cold water
• B is cold vapour
• C is hot water
• D is hot vapour

Generally, the latent heat of evaporation increases with decreasing temperature, so you need more energy to evaporate water at lower temperature. At water critical temperature near $$374 ^{\circ}\mathrm{C}$$ the properties of liquid and gaseous water converge to the same values and the latent heat of evaporation converges to zero.

If water at $$50^{\circ}\mathrm{C}$$ is provided by latent heat of evaporation at $$50^{\circ}\mathrm{C}$$, then it will evaporate. If water at $$50^{\circ}\mathrm{C}$$ is provided by latent heat of evaporation at $$100^{\circ}\mathrm{C}$$, then some water will not evaporate. Because the latent heat of evaporation is bigger at $$50^{\circ}\mathrm{C}$$, compared to $$100^{\circ}\mathrm{C}$$.

Technically, it is different question, as evaporation at ambient temperature takes energy from the environment, while you have to supply energy for the boiling.

Note that physicists/chemists prefer to talk about vapour, a gaseous phase of substance, that is not considered as a "permanent" gas. Steam is rather a technical/engineering/everydays term, covering pure water vapour, mixtures of vapour with gases like air, or the same with an aerosol of water or ice particles. See water phase diagram. Water vapour exists even at at mesosphere at altitude near 80 km at temperatures almost $$-100^{\circ}\mathrm{C}$$. Also, ice can sublimate directly into vapour, without melting.

• You can calculate it, using heat capacities of vapour a water, as above. Aug 20 '20 at 14:37
• This is an excellent answer. Just to clarify though, what do you mean when you say " At water critical temperature near 374∘C the properties of liquid and gaseous water converge to the same values and the latent heat of evaporation converges to zero." Surely at T=374 C, the latent heat of evaporation of water does not converge to zero but rather it converges to the latent heat of vaporization of water at T=374 C which is around $41 kJ/mol$, not zero? Jun 6 at 12:14
• @SalahTheGoat There is no evaporation at the critical temperature nor above, therefore the latent heat of evaporation is defined for T<Tc. The left limit of its value for T approaching Tc is 0 kJ/mol. Think about it: Why should there be any need of supplying energy to have exactly the same state as before ? Remember that state variables change near critical conditions highly non linearly Jun 6 at 12:38
• Aha okay I understand now. So by critical point you're referring to $T \approx 374 C$ and $P\approx 217 atm$, the point where liquid/vapour H20 becomes a supercritical fluid correct? Thanks again for the great response. Jun 6 at 13:03