Suppose the initial temperature of a substance is 0 degree celsius. The temperature then increases, to 20 degree celsius.

So here's the question. What is the temperature difference between the two, in Kelvin?

I wince at the thought, but is it possible, given a low enough temperature, for urine to freeze instantly into an icicle if you're caught short in Arctic conditions. If so, how cold would it have to be? and could it be dangerous for an intrepid explorer? 

I've been told that temperature can be explained by how fast molecules are moving around, the higher the temperature the faster they move and the more kinetic energy they have.  This is however confusing as different molecules will move around at different paces and will exist as different states at the same temperature i.e. at room temperature oxygen will be a gas whereas molecules in a chair will be solid.

 Therefore how do you define temperature?

I've been dropping squash balls at different temperatures from a constant height of 1m, and measuring the height they bounce up to. I understand that as you heat the squash balls, air molecules inside the ball (which has negligible increases in mass and volume) bounce again each other and the inside of the ball more often and harder, leading to more air pressure in the ball, and thus a higher bounce. Is there any equation that links pressure or temperature with a drop height and bounce height? I've been using Boyle's law, Charles law and the pressure law to find pressure, and there are existing formulae for volumes, of course, but how can I link pressure with bounce? I assume it will involve the coefficient of restitution somewhere, but I'm unsure. Thanks a lot! :)

I have found that when I hang A4 sheets of paper by one thumbtack in the top center of the paper, the sides of the paper curve inwards after a few days. However, when I stuck A4 paper up beside a lightbulb, it didn't curve at all. I was wondering if this was caused by temperature. Is this correct, and if so, why?

Sometimes I get into bed and realise that I've filled up my hot water bottle with water that is too hot. I then add a little water from a nearby jug which is at room temperature. This cools down the temperature immediately, but the hot water I filled it with is still in the hot water bottle. So does the total amount of heat I get over the whole night change?