Mechanical waves transfer energy by inducing vibrations in the propagation medium.
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The extrapolated temperature is used to define the maximum temperature of the mixture relatively than the highest recorded temperature in which the conclusion will effect in a higher specific heat value. Heat is bound to escape from whatever apparatus is using, therefore it is needed to account for the loss of the heat that does not go into increasing the temperature of the mixture.
All of the above, work is a measurement of energy transfer, in Joules.
Potential energy = Joules
Kinetic energy = Joules
The key thing here is that anything having to do with just energy or energy transfer is measured in joules.
