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favorite mug is the best for breaking the laws of physics and generating infinite energy - though the blanket and the candle also have infinite heat, the mug would be the most versatile, as you could fill it with a super-hot liquid, then treat it like an RTG, generating electricity from the temperature difference between the mug and its environment. use the mug as your spaceship's power supply, and you'll never even need big honkin photovoltaic panels !
I love how this post was meant to be cozy, and the first thing you think of is breaking reality.
I would pick the candle!
Yeah infinite energy source was my first thought as well (mug/candle). Might be able to come up with some amazing uses for the blanket as well.
Candle. Infinite energy, plus no stress.
How does one recuperate the energy from a candle to transform it to something useful? Also, would it's output be enough to power anything meaningful in a reasonable time anyway?
According to this a burning candle releases about 80 watts.
It could operate a Sterling engine .
Assuming most of the candle's energy is released as heat, with light and magic making up a small percentage, and assuming a perfectly efficient engine, and a spherical cow for good measure...
You could charge your phone, or a power bank. You could power a light bulb. You could heat up water (for a flow of 2 milliliters per second, you could raise the temperature by about 10 degrees Celsius).
This is the right answer
With the blanket you can walk on the sun though. (Assuming that you won't get crushed by gravity)
Hate to burst your bubble, but the favorite mug is actually just a perfect insulator. Energy go in, energy no come out.