I can find the conversion easy enough, but I want to understand the fundamentals behind it. How do we KNOW that 4.184 J are in a cal? I'm learning thermodynamics and my book neglects to mention this(yet), and I'm getting hung up on it. I am having difficulty understanding how temperature translates into work this way. Temperature is the average kinetic energy of the system, I can see how they are related, but I'm just not understanding how you can experimentally show that 4.184 kg m2/s2 would raise the temperature of 1g of water 1°C.