Bathtub and shower valves have (and are required to have) anti-scald features which limit the temperature. Depending on the valve that may be somewhat adjustable - check the owners manual for it (look up on the web if you don't have one.)

I believe the reasoning is that a small child or invalid would not be able to get out of the tub, while it's assumed that they could pull their hands away from a sink. It is in response to actual burn incidents.

Different water temperature in different faucets
Let say I directly connect a small engine to my bicycle, and that I'm superman who can overcome any force.
Then I start cycling (using my legs...) - the engine starts to rotate, even though I haven't "started it" using the switch.

Does it mean that if I press the pedal (or whatever) of the engine, it will apply force? Either on a diesel or a gasoline engine.

Another question: Lets say I'm driving down a hill in a relatively high speed in a car, and I'm not pressing the gas pedal at all. Does the engine burn fuel at all, in both diesel and gas? If I (while in gear) turn off the engine, will something actually happen? If I would press the pedal after turning it off (while it still rotates) - will it apply force? (in both diesel and gas).

If, while driving, I disconnected the idler (i.e the engine won't apply any force if I'm not pressing the pedal at any RPM and pressing the clutch will take it to zero RPM) and press the brake until I get to a complete stop, will the engine "stall"? If I'm doing it in a hill facing down, after releasing the brakes I'd accelerate and the engine would gain RPMs, will it be able to continue applying force?

Finally: What's the difference between a "running engine" and one thats not running, assuming both are rotating?

I'm sorry if I'm asking too much so if you would at least explain the principle I'd be very happy. Thank you!
