Heat and Internal Energy

experiments performed by James Joule and others showed that energy may be added to (or removed from) a system either by heat or by doing work on the system (or having the system do work) .
It is important to make a major distinction between internal energy and heat. Internal energy is all the energy of a system that is associated with its microscopic components—atoms and molecules—when viewed
from a reference frame at rest with respect to the object. 
Heat is defined as the transfer of energy across the boundary of a system due to a temperature difference between the system and its surroundings.
It is also important to recognize that the internal energy of a system can be
changed even when no energy is transferred by heat. For example, when a gas is
compressed by a piston, the gas is warmed and its internal energy increases, but no
transfer of energy by heat from the surroundings to the gas has occurred. If the gas then expands rapidly, it cools and its internal energy decreases, but no transfer of energy by heat from it to the surroundings has taken place.
The temperature changes in the gas are due not to a difference in temperature between the gas and its surroundings but rather to the compression and the expansion. In each case, energy is transferred to or from the gas by work, and the energy change within the system is an increase or decrease of internal energy. The changes in internal energy in these examples are evidenced by corresponding changes in the temperature of the gas.
The Mechanical Equivalent of Heat
The system of interest is the water in a thermally insulated container. Work is done on the water by a rotating paddle wheel, which is driven by heavy blocks falling at a constant speed. The stirred water is warmed due to the friction between it and the paddles. If the energy lost in the bearings and through the walls is ne-
glected, then the loss in potential energy associated with the blocks equals the work done by the paddle wheel on the water. If the two blocks fall through a distance h, the loss in potential energy is 2mgh, where m is the mass of one block; it is this energy that causes the temperature of the water to increase. By varying the conditions
of the experiment, Joule found that the loss in mechanical energy 2mgh is propor-
tional to the increase in water temperature Δ T. The proportionality constant was found to be approximately 4.18 J/g.°C. Hence, 4.18J of mechanical energy raises the temperature of 1g of water by 1°C. More precise measurements taken later demonstrated the proportionality to be 4.186 J/g.°C when the temperature of the water was raised from 14.5°C to 15.5°C. We adopt this “15-degree calorie” value: 1 cal = 4.186 J .


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