Heat and Thermodynamics

Question 1: Discuss latent heat and specific heat as they relate to phase and temperature changes.

Answer 1: Suppose we wish to convert ice initially at -5 °C to water at 5 °C. We must provide heat to accomplish this. The amount of heat required to raise the temperature of a given quantity of a material is a property known as specific heat. This is most often given on a mass basis, with units of J/g-K, but may also be given as a molar property as J/mol-K. If the given quantity of material and the given specific heat are not unit compatible, it will be necessary to multiply or divide by the molar weight of the material to achieve compatibility. Returning to the problem at hand, in order for ice initially at -5 °C to reach 5 °C, it must undergo a phase change, from a solid to a liquid. When the ice is heated, it does not simply become water when it reaches 0 °C. In order for the ice to become water, additional heat must be added to break the bonds of the solid. This heat is called the latent heat of fusion and, like the specific heat, may be given on a mass or a molar basis, with common units of kJ/g or kJ/mol, respectively. This heat input for the phase change occurs while the material remains at a constant temperature. Once the phase change has been completed, the water temperature will begin to rise again with heat input, though the specific heat of liquid water will be different from that of ice. If the water need be heated above 100 °C, it will have to undergo a second phase change, overcoming the latent heat of vaporization, and its temperature will subsequently be governed by a third specific heat, that of the gas phase.

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Question 2: Discuss heat transfer by conduction.

Answer 2: Heat always flows from a region of higher temperature to a region of lower temperature. If two regions are at the same temperature, there is a thermal equilibrium between them and there will be no net heat transfer between them. Conduction is a form of heat transfer that requires contact. Since heat is a measure of kinetic energy, most commonly vibration, at the atomic level, it may be transferred from one location to another or one object to another by contact. The rate at which heat is transferred is proportional to the material’s thermal conductivity k, cross-sectional area A, and temperature gradient dT/dx, q = kA(dT/dx). If two ends of a rod are each held at a constant temperature, the heat transfer through the rod will be given as q = kA(TH – TL)/d, where d is the length of the rod. The heat will flow from the hot end to the cold end. The thermal conductivity is generally given in units of W/m-K. Metals are some of the best conductors, many having a thermal conductivity around 400 W/m-K. The thermal conductivity of wood is very small, generally less than 0.5 W/m-k. Diamond is extremely thermally conductive and may have a conductivity of over 2,000 W/m-k. Although fluids also have thermal conductivity, they will tend to transfer heat primarily through convection.

Question 3: Discuss heat transfer by convection, both free and forced.

Answer 3: Heat always flows from a region of higher temperature to a region of lower temperature. If two regions are at the same temperature, there is a thermal equilibrium between them and there will be no net heat transfer between them. Convection is a mode of heat transfer in which a surface in contact with a fluid experiences a heat flow. The heat rate for convection is given as q = hA?T, where h is the convection coefficient. The convection coefficient is dependent on a number of factors, including the configuration of the surface and the nature and velocity of the fluid. For complicated configurations, it often has to be determined experimentally. Convection may be classified as either free or forced. In free convection, when a surface transfers heat to the surrounding air, the heated air becomes less dense and rises, allowing cooler air to descend and come into contact with the surface. Free convection may also be called natural convection. Forced convection in this example would involve forcibly cycling the air: for instance, with a fan. While this does generally require an additional input of work, the convection coefficient is always greater for forced convection.

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