Voltage, capacity, and energy

Open-circuit voltage reflects the electrode potential difference and chemical state after rest, whereas terminal voltage also includes ohmic drop, charge-transfer polarization, and concentration polarization caused by current. During charge terminal voltage is generally above the equilibrium value at the same state of charge; during discharge it is below, and it relaxes after current stops. Material papers commonly report half-cell potential versus Na/Na+, while a commercial full cell reports the difference between cathode and anode; these are not the same number. Nominal voltage is a representative value for system design, whereas upper charge and lower discharge voltages are control limits.

Capacity is the charge passed during a defined charge or discharge interval and is commonly expressed in ampere-hours (Ah); one ampere-hour is the charge delivered by one ampere for one hour. Cell capacity is set by whichever electrode reaches its limit first, the cyclable sodium inventory, and voltage cutoffs. At lower temperature, higher rate, or after ageing, stronger polarization brings the cell to cutoff earlier and measured capacity falls, without necessarily meaning all active material is permanently lost. A capacity comparison needs charge or discharge direction, temperature, rate, SOC window, rest protocol, and cycle number.

Accurate discharge energy can be written as E = ∫V dQ: energy is the integral of voltage over each increment of charge along the discharge curve, commonly expressed in watt-hours. If the voltage plateau is flat, nominal voltage multiplied by capacity can be a useful engineering estimate. If the curve slopes strongly, rate is high, or temperature is low, average discharge voltage changes and the simple product becomes less accurate. Two 100 Ah cells with different average voltage deliver different energy. Conversely, watt-hours alone do not reveal maximum power or transient voltage drop.

Cathode specific capacity normally uses cathode active-material mass as the denominator, while hard-carbon specific capacity uses anode active-material mass. Energy based on both active materials includes cathode and anode mass. Commercial-cell Wh/kg also counts collectors, electrolyte, separator, and enclosure; pack values additionally count structures, BMS, and connections. If denominators differ, values cannot be compared directly even when every line says Wh/kg. This page establishes the basic voltage-capacity-energy relation; comparisons between material, cell, and pack specific-energy values continue in the dedicated energy-metrics topic.

Start with nominal, upper, and lower voltage. Then identify the temperature, rate, and cutoff behind capacity. Multiply nominal voltage by capacity as a plausibility check on rated energy, and look for measured discharge energy, cell mass, and dimensions. For cycle life, identify whether end of life means 80%, 70%, or another remaining capacity. For fast charge, identify the charged percentage and starting and ending SOC. For cold performance, distinguish charging from discharging. In research papers, also inspect areal capacity, compaction density, N/P ratio, and electrolyte quantity. If one link in this chain is missing, treat the number as a parameter needing conditions rather than a conclusion across products.