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When looking at the Wikipedia page for Lithium-ion batteries, one can see that there are some technical details such as Specific Energy and Specific Power, but I don't know how to connect them.

For example, one can see this:

Specific Energy: 100–265 Wh/kg

and

Specific Power: 250 - 340 W/kg

According to the theory, power equals energy divided by time; i.e. 1 W = 1 Wh/t. So can guess that t is the discharge time. Li-ion batteries usually have a discharge rate of 1 C, which means that the battery would be discharged in around one hour. Looking at those numbers, it doesn't look like my logic is correct, therefore I would like to know if this is the case or if those numbers don't really match?

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  • $\begingroup$ It's not theory: it's definition. Energy = $\int Power*dt$ . As the battery discharges, it's internal resistance changes, so voltage changes, and so on $\endgroup$
    – Carl Witthoft
    Commented Feb 1, 2018 at 19:16
  • $\begingroup$ The power is instantaneous power for a fully charged battery. That rate can not be sustained for a whole hour. Based on the energy you might expect roughly a half hour at that discharge rate. $\endgroup$
    – agentp
    Commented Feb 1, 2018 at 19:23

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Batteries can't deliver unlimited current. Internal resistance, and limitations of the chemical reaction within the battery make that it can only deliver so much current. And the more current is drawn, the bigger the voltage drop will be because of above mentioned reasons.

Specific power (W/kg) and capacity, specific charge or specific energy(Wh/kg or J/kg) are pretty much totally unrelated. You can compare it with humans. Let's take two athletes. Usain Bolt is able to run faster than a lightning bolt for 100 metres, but Phidippides is able to run 42km in one run. Both persons are about the same weight/size. The first says something about specific power, the latter about capacity. They can't compete with each other.

Battery A may be able to store only enough charge to power a lightbulb for 1 minute, while still being able to deliver 100 Ampere if needed. Battery B may be able to store enough energy to power the exact same bulb for an hour, while only being able to deliver 1 Ampere if needed.

Some battery types like LiPo's can deliver much current, and without having too much voltage drop. Li-ion batteries perform somewhat less, but can store a slightly bigger charge at the same size of a LiPo.

Specific power means how much power a (one-celled)battery can deliver at a certain weight. So a Li-ion cell of 1 kg is on average able to deliver 300W. It doesn't matter how long you will need to consume power before recharging, you just can't get more power out of that cell. It's intrinsic capabilities limit that.

More expensive batteries may deliver more, but it's an average number. So in this analogy, if you need 600W, you just need 2kg of li-ion. Totally unrelated to that is the charge they can hold. It's just that there is a correlation most of the times, but not necessarily.

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