Electronic – ESR of Ceramic Capacitor

This unfortunately depends very much on the application. Most low ESR ('low Z'), low voltage (6.3V and lower) electrolytics (e.g. conductive polymer 'solid' capacitors, power supply output filter capacitors) are characterized at 100kHz. Other bulk capacitors (usually 10-63V) which explicitly give ESR in their datasheets are most often characterized at 10kHz. If your application requires knowledge of ESR, this is what you are looking for.

However, general purpose capacitors seldomly have ESR as a statistic in their datasheets. They often only have the loss tangent (tan \$\delta\$) in the datasheet. This is measured most often at 120Hz, but in some cases also at 1kHz. There is usually no use in trying to measure these capacitors at 10 or 100kHz, because the internal construction prioritizes volumetric capacity over impedance, and the ESL makes the capacitors virtually useless at higher frequencies.

And now I'm only talking about aluminum electrolytics - there are many more nuances to this story when you start looking at other build-ups, like metallized film and ceramic capacitors.

So to answer your question: ALL THE FREQUENCIES.

Large physical size will help dissipate power, but a large capacitor may also have large losses due to high ESR. Power supply capacitors sometimes have inverted ribs to increase the surface area and help them dissipate power (though I have not seen that in quite a while, Philips parts used to have them). Low-end capacitors are often physically smaller than those from reputable manufacturers for the same capacitance- avoid those where possible.

If you're scavenging stuff, you can try to look up the part numbers, or if it's no-name Asian stuff you might try to guess from the circuit function, but if the requirements are demanding, you might be better off to just go buy some parts of known specifications for a dollar or two. Generally even no-name parts will have the part capacitance, the working voltage, and a rated temperature marked on them.

A general rule is that the lifetime of an electrolytic capacitor will be at least 2,000 hours at the rated temperature (that's about a work-year). Some are rated for more life at the rated temperature. The temperature will almost always be marked on the capacitor- often 85°C or 105°C, but sometimes more.

The life doubles roughly for every 10°C you can reduce the temperature- internal heating via ESR losses contributes, but also external heating from other components and from the environment. If you want the thing to last a long time, use a high quality part and run it as cool as possible. If you want it to die fast, use a cheap part and run it hot.