Trying to calculate the energy efficiency of an electrolyses by using the formula: eff= HHV* hydrogen volume in ml / ( UIt). where U is voltage, I current, t is time and HHV is the higher heating value for hydrogen gas.
But I find different values for HHV in literature; Gross calorific value: 141.7 MJ/kg or 12.7MJ/m^3=127J/ml.
According to my experiment, U=31V, I=0.28A and t=20 minutes and hydrogen gas produced during 20 minutes is 45.1 ml.
if I use MJ/kg, the efficiency is more than 100 times which is very unrealistic but If I use J/ml for HHV I get the efficiency to be around 57% which is a reasonable considering the energy losses in an electrolyses.
Something that most people overlook when using chemical tables is that there should always be a reference temperature and pressure. If you change the reference (or don't account for your conditions), you will not get the correct result. The ASME PTC-22 committee argued about this for years, with representatives from the largest gas turbine manufacturers in the world getting the calculation wrong. I provided an Excel spreadsheet to the committee that yields the same heat balance results, regardless of the reference conditions. This same spreadsheet shows how hF and sF (enthalpy and entropy of formation) change with reference conditions. I always use the NASA Glenn Report for such properties. You should also be aware of the difference when using HHV and LHV. In this particular situation (electrolysis), the resulting H2O is in the liquid form, so HHV is appropriate. Many people incorrectly use HHV for combustion. If the resulting H2O is in the vapor state, then LHV is the appropriate quantity. The same goes for burning coal. Never use HHV for combustion, except perhaps in a bomb calorimeter. I suspect that there are other concerns for your particular problem. The temperature and pressure of the captured gas may be more difficult to determine than it seems (it may not be 1 atm at ambient temperature). Even small differences in pressure may impact your calculation of density, though I suspect it will have a compressibility, Z, of unity PV=ZRT. I should also mention that there are many tables on the Web that are incorrectly labeled, including mixtures of gram-mole and kg-mole. Any calculation involving J/ml requires a density, as heating value is always per mass. Reported gas densities can be a jumbled mess of units with vague or incorrect size of mole listed or implied. I've see J/g when they meant gram mole and not gram and J/mole when they meant kg mole and not gram mole.
Dudley J Benton well said and thanks for a great guide.
The temperature of the system of course changes as I am also using a radiation source to heat up the electrolyte solution while the DC current is applied to drive the system.
Temperature in this particular system goes from room temperature to around 80•c. This means that neither pressure nor the temperature is constant.
As 141.7MJ/kg of hydrogen is for the standard conditions, I have to make a curve of density of hydrogen vs temperature and then when average density available, it multiplies by 141.7NJ/kg to find j/ml.
Another possibility according to my idea is that, I use ideal gas law to find the number of moles from the given volume and the the mass in grams. Not so sure though, as the assumption of ideality might unrealistic.
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