Quick Heat is defined as the form of energy that is transferred across the boundary of a system at a given temperature to another system (or the surroundings) at a lower temperature by virtue of the temperature difference between the two systems. That is, heat is transferred from the system at the higher temperature to the system at the lower temperature, and the heat transfer occurs solely because of the temperature difference between the two systems.
Nomenclature
Q
heat, or heat transfer
q
specific heat transfer, or heat transfer per unit mass of the system
Q
rate of heat transfer, or heat transfer per unit time
If a block of hot copper is placed in a beaker of cold water, the block of copper cools down and the water warms up until the copper and water reach the same temperature. What causes this decrease in temperature of the copper and the increase in the temperature of the water? The result of the transfer of energy from the copper block to the water. This forms the basis for the definition of heat.
Another aspect of the definition of heat as described at the beginning of this lesson is that a body never contains heat. Rather, heat can be identified only as it crosses the boundary. Thus, heat is a transient phenomenon. If the hot block of copper is considered as one system and the cold water in the beaker as another system, it may be recognized that originally neither system contains any heat (they do contain energy, of course). When a copper block is placed in the water and the two are in thermal communication, heat is transferred from the copper to the water until equilibrium of temperature is established. At this point there is no longer heat transfer, because there is no temperature difference. Neither system conatains heat at the conclusion of the process. It also follows that heat is identified at the boundary of the system, for heat is defined as energy being transferred across the system boundary.
Units
Heat, like work, is a form of energy transfer to or from a system. Therefore, the units for heat, and to be more general, for any other form of energy as well, are the same as the units for work, or are at least directly proportional to them. In the International System the unit for heat (energy) is the joule. Similarly, in the English System, the foot pound force is an appropriate unit for heat. However, another unit came to be used naturally over the years, the result of an association with the process of heating water. Consider as a system 1 lbm of water at 59.5 F. Let a block of hot copper of appropriate mass and temperature be placed in the water so that when thermal equilibrium is established the temperature of the water is 60.5 F. This unit amount of heat transferred from the copper to the water in this process is called the British thermal unit (Btu). More specifically, it is called the 60-degree Btu, defined as the amount of heat required to raise 1 lbm of water from 59.5 F to 60.5 F. (The Btu as used today is actually defined in terms of the standard SI units.) It is worth noting here that a unit of heat in metric units, the calorie, originated naturally in a manner similar to the origin of the Btu in the English system.
Sign Convention
Heat transferred to a system is considered positive, and heat transferred from a system is negative. Thus, positive heat represents energy transferred to a system, and negative heat represents energy transferred from a system. The symbol Q may be used to represent heat.
Derivation
From a mathematical perspective, heat, like work, is a path function and is recognized as in inexact differential. That is, the amount of heat tranferred when a system undergoes a change from state 1 to state 2 depends on the path that the system follows during the change of state. Since heat is an inexact differential, the differential is written δQ. On integrating:
∫
2
1
δQ = 1Q2
1Q2 is the heat transferred during the given process between states 1 and 2. The rate at which heat is transferred to a system is designated by the symbol
Q
:
Q
≡
δQ
dt
It is also convenient to speak of the heat transfer per unit mass of the system q, often termed specific heat transfer, which is defined as:
q ≡
Q
m
Heat energy is created in the movement of atoms. Boiling water, burning wood, and rubbing your hands together really fast are all examples of heat energy. Geothermal, and passive solar are sources of heat energy, but biomass (a type of chemical energy) can be burned to produce heat energy.
