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Why does variation of Cp with temperature tends to a limit of ~3R?
Cp, also known as specific heat capacity, is the amount of heat required to raise the temperature of a substance by 1 degree Celsius. It is defined as the amount of heat energy needed to raise the temperature of 1 gram of a substance by 1 degree Celsius. Cp varies with temperature because different substances have different molecular structures and therefore require different amounts of energy to raise their temperature.
The variation of Cp with temperature affects heat transfer in two ways. First, as the temperature increases, the Cp of a substance generally increases as well. This means that more heat energy is required to raise the temperature of the substance, resulting in a slower rate of heat transfer. Second, the variation of Cp with temperature can also affect the direction of heat transfer. In some cases, the Cp of a substance may decrease with increasing temperature, causing heat to flow in the opposite direction.
The temperature limit in the variation of Cp refers to the temperature at which the Cp of a substance reaches its maximum or minimum value. This temperature limit is important because it marks a point at which the heat transfer characteristics of the substance may change. For example, if the temperature limit corresponds to a change in the state of the substance (e.g. solid to liquid), the heat transfer process may also change.
The variation of Cp with temperature is determined experimentally by measuring the heat transfer between a substance and its surroundings at different temperatures. The data collected is then plotted on a graph, with temperature on the x-axis and heat transfer on the y-axis. The resulting curve is known as the Cp vs. temperature curve and provides information about how Cp changes with temperature for the particular substance.
The variation of Cp with temperature is important in thermodynamics because it affects many processes and phenomena, such as heat transfer, phase changes, and chemical reactions. Understanding the variation of Cp with temperature allows scientists and engineers to predict and control these processes, leading to the development of new technologies and advancements in various fields.