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Heat In this chapter we examine the nature of heat, particularly the ways that it may be transferred. We also look at the 2nd law of thermodynamics, which is a fundamental law of nature with far-reaching implications. The nature of heat As mentioned in a previous chapter, heat can be thought of as the internal kinetic energy of the atoms and molecules that make up a substance. Being a form of energy, it is measured in the standard unit of Joule, but it is also commonly measured in the following units: calorie: this is the heat energy needed to raise 1 gm of water 1 oC. 1 calorie is equal to 4.186 Joules. Calorie: this is a common unit to measure the energy content of food, with 1 Calorie = 1000 calories. BTU: this is a British Thermal Unit, still used as a rating on some furnaces, and is the heat energy needed to raise 1 pound of water 1 oF. 1 BTU = 252 calories = 1,054 Joules. Temperature Heat refers to the total amount of heat energy in a substance - two liters of boiling water have more heat energy than one liter. Temperature, on the other hand, is a relative term, and refers to the average kinetic energy of the atoms and molecules in a substance. One fundamental property of temperature is that There are three main temperature scales used in the world - Celsius, Fahrenheit, and Kelvin. These are compared in the following table. One can see from this that the size of 1 oC and 1 K is the same, while both differ from the size of 1 oF; in fact, the difference between the Celsius scale and the Kelvin scale is simply a shift by 273 o. The Kelvin scale is more convenient to measure substances with very low temperatures. Moreover 0 Kelvin has a very deep physical significance: absolute zero, as the name suggests is the lowest temperature that can, even in principle, be achieved in Nature. It is the temperature associated with empty space that is completely devoid of all all motion and/or energy. In practice it is impossible to obtain, although one can get arbitrarily close. As we will see in the chapter on cosmology, not even the empty space between distance galaxies is at absolute zero: it contains energy and an associated temperature of about 2.7 Kelvin. Heat Capacity The heat capacity of a substance is a measure of how well the substance stores heat. Whenever we supply heat to a material, it will necessarily cause an increase in the materials temperature. The heat capacity is defined as the amount of heat required per unit increase in temperature, so that Thus, materials with large heat capacities, like water, hold heat well - their temperature wont rise much for a given amount of heat - whereas materials with small heat capacities, like copper, dont hold Table 8.1: Temperature scale comparisonsoC K oFWater boils 100 373 212Water freezes 0 273 32Absolute zero -273 0 -459heat well - their temperature will rise significantly when heat is added. Heat Transfer There are three ways that heat may be transferred between substances at different temperatures - conduction, convection, and radiation. We consider each of these in turn. Conduction Convection Radiation Conduction The flow of heat by conduction occurs via collisions between atoms and molecules in the substance and the subsequent transfer of kinetic energy. Let us consider two substances at different temperatures separated by a barrier which is subsequently removed, as in the following figure. Figure 8.1: Heat transfer by conductionWhen the barrier is removed, the fast (hot) atoms collide with the slow (cold) ones. In such collisions the faster atoms lose some speed and the slower ones gain speed; thus, the fast ones transfer some of their kinetic energy to the slow ones. This transfer of kinetic energy from the hot to the cold side is called a flow of heat through conduction. Different materials transfer heat by conduction at different rates - this is measured by the materials thermal conductivity. Suppose we place a material in between two reservoirs at different temperatures, as in the following figure. Figure 8.2: Measurement of thermal conductivityLet us now measure the flow of heat through the material over time. Knowing the materials cross-sectional area and length, the thermal conductivity of the material is then defined as Thus, for a given temperature difference between the reservoirs, materials with a large thermal conductivity will transfer large amounts of heat over time - such materials, like copper, are good thermal conductors. Conversely, materials with low thermal conductivities will transfer small amounts of heat over time - these materials, like concrete, are poor thermal conductors. This is why if you throw a piece of copper and a piece of concrete into a campfire, the copper will heat up much more quickly than the concrete.Instead of being rated in terms of thermal conductivity, insulation is therefore usually rated in terms of its thermal resistance, which is defined as Materials which have a high thermal conductivity have, by definition, a low thermal resistance - they are poor heat insulators. On the other hand, materials with a low thermal conductivity have a high thermal resistance - they are good heat insulators. Good insulating materials therefore should have a high thermal resistance. In fact, the R value quoted for insulation is the thermal resistance (in British units). Convection Convection is the flow of heat through a bulk, macroscopic movement of matter from a hot region to a cool region, as opposed to the microscopic transfer of heat between atoms involved with conduction. Suppose we consider heating up a local region of air. As this air heats, the molecules spread out, causing this region to become less dense than the surrounding, unheated air. For reasons discussed in the previous section, being less dense than the surrounding cooler air, the hot air will subsequently rise due to buoyant forces - this movement of hot air into a cooler region is then said to transfer heat by convection. Heating a pot of water on a stove is a good example of the transfer of heat by convection. When the stove is first turned on heat is transferred first by conduction between the element through the bottom of the pot to the water. However, eventually the water starts bubbling - these bubbles are actually local regions of hot water rising to the surface, thereby transferring heat from the hot water at the bottom to the cooler water at the top by convection. At the same time, the cooler, more dense water at the top will sink to the bottom, where it is subsequently heated. These convection currents are illustrated in the following figure. Figure 8.3: Convection currents in boiling waterConsider now two regions separated by a barrier, one at a higher pressure relative to the other, and subsequently remove the barrier, as in the following figure. These convection currents are illustrated in the following figure. Figure 8.4: Flow of material through a pressure differenceWhen the barrier is removed, material in the high pressure (high density) area will flow to the low pressure (low density) area. If the low pressure region was originally created by heating of the material, one sees that movement of material in this way is an example of heat flow by convection. Radiation The third and last form of heat transfer we shall consider is that of radiation, which in this context means light (visible or not). This is the means by which heat is transferred, for example, from the sun to the earth through mostly empty space - such a transfer cannot occur via convection nor conduction, which require the movement of material from one place to another or the collisions of molecules within the material. Often the energy of heat can go into making light, such as that coming fro
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