What's the relation between temperature change and energy change?

Question

I need to determine the power of given settings of a sonication machine. I came up with the idea of sonicating a volume of water and measuring the temperature difference after a set amount of sonication time, at a given setting. How do I correlate the change in temperature to the change in energy, (which can then be correlated to electrical power, or current or whatever.) I remember something vaguely involving entropy being the derivative of energy with respect to Absolute Temperature.+

Answer 1

You need to know the weight of water. The energy required to raise the temperature is:

Q = m*c*(T1-T0)

m is the mass of water
c is a constant (1 BTU per pound)
T1 is you final temp
T0 is your starting temp

So if you raise 1 gallon of water (8.3 lbs) by 10 degrees, the energy would be 83 BTU's

Answer 2

Measure the temperature change and knowing the volume of water you have you see how much energy the water was given using the specific heat of water. The peoblem is you'll have to account for heat loss from the water to the environment.

Answer 3

E=kt

Answer 4

Ek = 1.5kT where k is the Boltzmann constant