![]() As the hot water begins to cool and the cold water begins to warm, the difference in their temperatures decrease and the rate of heat transfer decreases. The two containers have a 65☌ difference in temperature. Initially, when the rate of heat transfer is high, the hot water has a temperature of 70☌ and the cold water has a temperature of 5☌. What variable contributes to this decrease in the heat transfer rate over the course of time? Answer: the difference in temperature between the two containers of water. And as time progresses, the slopes of the lines are becoming less steep and more gently sloped. Initially heat is being transferred at a high rate as reflected by the steeper slopes. Over the course of time, the rate of heat transfer is decreasing. So we can think of the slopes as being a measure of the rate of heat transfer. When the two samples reach thermal equilibrium, there is no more heat transfer and the slope is zero. The temperature of a sample changes more rapidly if heat is transferred at a high rate and less rapidly if heat is transferred at a low rate. The rate at which temperature changes is proportional to the rate at which heat is transferred. The cold water is gaining energy, so its slope is positive. The hot water is losing energy, so its slope is negative. The temperature is changing because of the heat transfer from the hot to the cold water. In the graphs above, the slope of the line represents the rate at which the temperature of each individual sample of water is changing. If the two water samples are equipped with temperature probes that record changes in temperature with respect to time, then the following graphs are produced. Earlier in this lesson, we discussed the transfer of heat for a situation involving a metal can containing high temperature water that was placed within a Styrofoam cup containing low temperature water. Once the two locations have reached the same temperature, thermal equilibrium is established and the heat transfer stops. The transfer of heat will continue as long as there is a difference in temperature between the two locations. In conduction, heat is transferred from a hot temperature location to a cold temperature location. Once the variables affecting the rate of heat transfer are discussed, we will look at a mathematical equation that expresses the dependence of rate upon these variables. Our discussion will be restricted to the variables affecting the rate of heat transfer by conduction. So what variables would affect the heat transfer rates? How can the rate of heat transfer be controlled? These are the questions to be discussed on this page of Lesson 1. Attention must be given to increasing heat transfer rates in the reactor and in the turbine and decreasing heat transfer rates in the pipes between the reactor and the turbine. The challenge is to efficiently transfer the heat to the water and to the steam turbine with as little loss as possible. The heat is transferred to water and the water carries the heat to a steam turbine (or other type of electrical generator) where the electricity is produced. The method involves generating heat in a reactor. Household electricity is most frequently manufactured by using fossil fuels or nuclear fuels. As another example, consider electricity generation. We make efforts to reduce this heat loss by adding better insulation to walls and attics, caulking windows and doors, and buying high efficiency windows and doors. Heat escapes from higher temperature homes to the lower temperature outdoors through walls, ceilings, windows and doors. For instance, those of us who live in colder winter climates are in constant pursuit of methods of keeping our homes warm without spending too much money. This topic is of great importance because of the frequent need to either increase or decrease the rate at which heat flows between two locations. Now we will investigate the topic of the rate of heat transfer. The three main methods of heat transfer - conduction, convection and radiation - were discussed in detail on the previous page. On previous pages of this lesson, we have learned that heat is a form of energy transfer from a high temperature location to a low temperature location.
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