Physics
Newton's Law of Cooling
Newton's Law of Cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. This law is often used to model the cooling of hot objects in a cooler environment, such as a cup of coffee cooling down in a room.
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4 Key excerpts on "Newton's Law of Cooling"
- Yuefan Deng(Author)
- 2017(Publication Date)
- World Scientific(Publisher)
68 Chapter 2 Mathematical Models 2.1 Newton’s Law of Cooling Newton’s law of cooling was introduced by Isaac Newton ሺDecember 25, 1642 –March 20, 1726ሻ in 1701 to describe convection cooling, in which the heat transfer coefficient is independent or almost independent of the temperature difference between the object and its thermo environment. For cases where the temperature difference is too big to maintain such assumptions, two French Physicists, P. Dulong and A. Petit, introduced corrections to the original Newton’s law of cooling in 1817. The time rate of change of the temperature ܶሺ ݐ ሻ of an object is proportional to the difference between ܶሺ ݐ ሻ and the temperature ܣ 2.1 Newton’s Law of Cooling 69 of the surrounding medium. The medium is assumed to be so big that the heat transfer to the medium from the object, or the reverse, is too insignificant to change the medium’s temperature. However, such heat transfer will cause the object’s temperature to change, and this is the subject of Newton’s law of cooling published anonymously in Philosophical Transactions. Our current discussion is an approximation of the truth that the total energy is conserved for the complete system of the body and the medium. Figure 2.1 Placing an object of temperature ܶ into a large medium of fixed temperature ܣ. Consider an object at a temperature ܶሺ ݐ ሻ that is placed in a medium at a constant temperature ܣ ሺFigure 2.1ሻ. We establish the DE that describes the temperature change of the object while it exchanges energy ሺheatሻ with the medium. We define a few quantities: ܣ is the temperature of the medium, kept at a constant; ܶሺ ݐ ሻ is the temperature of the object at time ݐ; ܶሺ ݐ ൌ 0ሻ ൌ ܶ is the initial temperature of the object; ݐ is the time; ௗ ்ሺ௧ሻ ௗ ௧ ൌ ݇ሺ ܣ െ ܶሻ is the rate of temperature variation and ݇ is a constant parameter that characterizes the heat conductivity of the medium with the object.
eBook - PDFThe Silicon Web
Physics for the Internet Age
- Michael G. Raymer(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
Heat does not flow. That would be a misuse of language. In addition, when we talk of the heat capacity of an object, we do not mean how much heat the object can contain (that makes no sense grammatically). We mean how much thermal energy can be trans-ferred to the object, in connection with a certain change of the object’s temperature. THINK AGAIN It might be tempting to think that thermal energy and temperature are the same concept, because the change of temperature is proportional to the change in thermal energy. This is not the case. To see this, compare 1 cup of water to 1 gallon (16 cups) of water, both initially at room temperature. Now put both of these onto identical stove burners for equal lengths of time, thereby increasing the thermal energy contained in each by the same amount. If the gallon of water becomes warm to the touch, the cup of water will become very hot. The temperatures are not equal, although the thermal energy increases are equal. How fast does thermal energy transfer? That is, what is the rate of thermal energy transfer? Newton hypothesized that the rate of thermal energy transfer from one object to another is proportional to the difference of the temperatures of the two objects. This is correct, and we call this Newton’s law of cooling. Newton’s law of cooling: The rate of thermal energy transfer (J/sec), from one object at tempera-ture T A to another object at temperature T B , is proportional to the difference in temperature. That is, (Rate of thermal energy flow from object A to object B ) ∝ ( T A – T B ) This equation summarizes the obvious fact that if object A is hotter than object B (i.e., T A > T B ), and they are put into contact, then thermal energy will flow from object A into object B . On the other hand, if T A is smaller than T B , then the rate of flow is negative, meaning thermal energy flows in the reverse direction—from object B to object A .
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
The motion of the molecules is related to the temperature of the liquid. A connection was thus forged between the everyday world and the tiny, invisible building blocks that make up this world. Thermodynamics also addresses more practical questions. Have you ever wondered how a refrigerator is able to cool its contents, or what types of transformations occur in a power plant or in the engine of your automo- bile, or what happens to the kinetic energy of a moving object when the object comes to rest? The laws of thermodynamics can be used to provide explanations for these and other phenomena. ■ Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 482 Temperature 18 18.1 Temperature and the Zeroth Law of Thermodynamics 18.2 Thermometers and the Celsius Temperature Scale 18.3 The Constant-Volume Gas Thermometer and the Absolute Temperature Scale 18.4 Thermal Expansion of Solids and Liquids 18.5 Macroscopic Description of an Ideal Gas STORYLINE You have discovered that you are out of potato chips. While driving to the store, you look at the high-voltage electric power transmis- sion lines crossing the road ahead of you. You have seen these lines almost every day, but there is something different about them today. The power lines between the towers on either side of the road seem to be sagging lower today than they have in the past. Then you notice that a brick sidewalk on the side of the road has buckled, as shown above.
eBook - PDFIntroduction to Physics
Mechanics, Hydrodynamics Thermodynamics
- P. Frauenfelder, P. Huber(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
C H A P T E R 7 BASIC CONCEPTS OF T H E R M O D Y N A M I C S 6 3 . INTRODUCTION The science of mechanics is based on the three laws of Newton, which form the basis for the calculation of the motions of single particles and of sys-tems of particles. We postulate that these laws are unrestricted in their validity for non-atomic phenomena, in contrast to empirical laws such as Hooke's law and the laws of friction. Newton's laws are characterized by the absence of any empirical constants, and by the fact that they make no assumptions regarding the structure of matter. In an exactly analogous way, the science of thermodynamics is based on certain general laws, known as the three laws of thermodynamics.^ Like Newton's laws, the laws of thermodynamics contain no empirical constants and involve no assumptions regarding the structure of matter. Hence, they may be universally applied to all physical phenomena without the results being dependent upon the properties of the substances being studied. Just as Newton's laws are used to derive relations between the quantities characterizing the mechanical properties of matter (mass and momentum, stress and strain, etc.), so the laws of thermodynamics are used to obtain relations between the quantities describing the thermodynamic state of a system. In general, empirical constants appear in these relations. Thus, this aspect of thermodynamics is also similar to the application of Newton's laws in mechanics. The molecular structure of matter provides a basis for understanding these empirical constants and their interrelations. The study of those pro-perties of matter that depend on some of the simpler consequences of the assumption that the constituent molecules are in constant motion is known as kinetic theory. The name derives from the fact that some properties of matter (e.g.: pressure, viscosity, temperature) can be explained as mani-festations of the kinetic energy of the constituent molecules.
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