Question

My question is the following: how much energy does it take to evaporate a liquid at constant volume?

For constant pressure, it’s very easy: Q = ΔHvap (Q in J/mol). However, the enthalpy of vaporization con only be used at constant pressure and isothermal evaporation, so what about isochoric evaporation, where both pressure (corresponding to vapor pressure) and temperature increase along the liquid-gas phase boundary during the heating process? Yet I still must rely on ΔHvap, because it's the only tabulated value available most of times.

More in detail, let us imagine that we have a sealed container with liquid in it and that we supply heat until all liquid has become vapor. For simplicity, let us forget that the liquid initially occupied part of the available volume.

I have thought of two methods but I am not sure whether they make sense:

One approach is to perform two transformations to go from the initial state to the final one. First, isothermal evaporation at constant volume: Q = ΔU = ΔHvap - pΔV. Second, temperature increase: Q = ΔU = cvΔT.

A second approach involves three steps: First, evaporation at constant temperature and pressure: Q = ΔHvap. Second, isobaric temperature increase: Q = cpΔT. Third, isothermal compression: Q = 0? The work is given back to the external environment in form of heat.

Any ideas or clarifications? Thank you!

Answer 1

When a liquid evaporates at constant volume, the amount of energy required can be calculated using the enthalpy of vaporization. This value represents the energy needed to vaporize the liquid and is typically tabulated at constant pressure and isothermal conditions. For isochoric evaporation, you can use a two-step or three-step approach to calculate the energy required.

Step-by-step explanation:

When a liquid evaporates at constant volume, the process is known as isochoric evaporation. In this case, both the pressure and temperature increase along the liquid-gas phase boundary during the heating process.

However, the enthalpy of vaporization (ΔHvap) is still the most relevant value to consider, as it represents the amount of energy required to vaporize the liquid. Although it is typically tabulated at constant pressure and isothermal conditions, it can still be used for isochoric evaporation.

To calculate the energy required for isochoric evaporation, you can use the two-step approach you mentioned.

The first step is isothermal evaporation at constant volume (Q = ΔU = ΔHvap - pΔV),

and the second step is temperature increase at constant volume (Q = ΔU = cvΔT).

Alternatively, you can also use a three-step approach.

The first step is evaporation at constant temperature and pressure (Q = ΔHvap),

the second step is isobaric temperature increase (Q = cpΔT),

and the third step is isothermal compression (Q = 0). In this case, the work done during compression is given back to the external environment in the form of heat.