Split water into hydrogen and oxygen and watch the two tubes fill in a 2 : 1 ratio. Turn the voltage, electrolyte, temperature and electrodes and see where the volts go: the thermodynamic minimum, the overpotentials and the resistance of the liquid.
-cell current
-voltage budget: E_rev + cathode + anode + I R
-gas collected
-hydrogen rate | cell resistance
-voltage efficiency
-heat released in the cell
The science
Electrolysis. Passing a current through acidified water splits it: at the cathode (negative) 4 H+ + 4 e- -> 2 H2, at the anode (positive) 2 H2O -> O2 + 4 H+ + 4 e-. For every 4 electrons, 2 H2 and 1 O2 form, so the hydrogen tube fills twice as fast as the oxygen tube.
Faraday's law. The amount of gas is set by the charge: n(H2) = I t / (2F), n(O2) = I t / (4F), F = 96 485 C/mol (100 % current efficiency assumed). The gas is collected over water, so its volume is V = n R T / (p - p_w), with p = 101.3 kPa and p_w the water vapour pressure (Magnus formula, 3.17 kPa at 25 C). One ampere gives about 7.6 mL of hydrogen per minute at 25 C.
Voltage budget. The supply voltage pays for four things: V = E_rev + eta_c + eta_a + I R. E_rev = (dH - T dS)/2F = 1.229 V at 25 C is the thermodynamic minimum (it falls about 0.85 mV per kelvin). The overpotentials follow the Butler-Volmer high-field form eta = (RT/alpha F) asinh(I / 2 I0), which is Tafel's law (+0.118 V per tenfold current at alpha = 0.5) when the current is large. The solution resistance is R = d / (kappa A), with the electrode spacing d, area A and conductivity kappa of the acid. The simulator solves this equation for the current by bisection.
Efficiency and heat. Splitting water needs the enthalpy dH = 285.8 kJ/mol, i.e. 1.481 V (the thermoneutral voltage). Above it the extra electrical energy I (V - 1.481) is released as heat in the cell; the voltage efficiency here is 1.481 V / V. Below it (1.23 to 1.48 V) the reaction takes the rest from the surroundings.
Simplifications and illustrative numbers. The exchange current densities of platinum, nickel and graphite, the conductivity curve of the acid (kappa = 0.45 c exp(-c/6) S/cm, peaking at high concentration) and its 2 %/K temperature coefficient are typical orders of magnitude, not measurements. Bubble screening of the electrodes, gas dissolution, the pressure difference from the water column, and the oxygen reduction at the cathode are ignored. The glass tubes are drawn wider than real so the levels are easy to see; the graduation shows 0-50 mL.