Suppose we drop a lead ball of mass M into water of mass m from a height h and allow everything to settle down. What is the temperature change of the water? Assume that the container is well insulated.
Potential Energy = mgh
dU = mcdT
where dU is the change in thermal energy, m is mass, g is gravitational constant, h is height, c is specific heat, dT is temperature change.
The Attempt at a Solution
In this case, I actually fully solved the problem. Just apply conservation of energy, and you'll get a neat formula. The only thing I'm confused about is that I had to make a sneaky assumption that the change in temperature of the water is the same as the change in temperature of the lead ball. I do not see that this is justified. Could someone explain why this assumption is valid?