Heat Flow at Equilibrium ```Name: Rachel Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: Is it possible for heat to flow between two objects with the same internal energy? Replies: Yes. But the amount of energy flowing in each direction is equal so, there is no net flow between the bodies. R. Avakian Rachel, It is possible because internal energy is not temperature. Two objects of different size or different material can have the same internal energy but different temperatures. When in contact, heat will flow from the object with the higher temperature to the object with the lower temperature. One thing to remember here is that "heat flow" as stated is a total effect. In reality, some heat does flow from cold to hot, but much more will flow from hot to cold. The total effect is heat from the hotter object to the colder object. Dr. Ken Mellendorf The answer is absolutely yes! The driving force for heat transfer is temperature, not internal energy. Internal energy is an 'extensive property' -- which means it depends on the amount of material present. Internal energy includes not only the kinetic energy of molecules (related to temperature), but also the potential energy stored in chemical bonds. If you double the amount of a given material, you also double the internal energy. Temperature is an 'intensive property' -- it does not depend on the amount of material present. If you have material of a given temperature, it is the same temperature if you add or take away the same material. So, if you have two materials at the same temperature, there is no driving force for heat transfer. However, you can have two materials with different temperatures, but the same internal energy, and there would be heat transfer. The two materials will be in thermal equilibrium when they reach the same temperature, not the same internal energy. Hope this helps, Burr Zimmerman Sure it is possible. Heat flows from objects at high temperature to objects at low temperature. Internal energy is an extensive quantity: it depends on how much stuff you have. So for the simplest example, let us say you have a kilogram of water and ten kilograms of water, each with the same internal energy. Which has the higher temperature? The one-kilogram sample! So it will transfer heat to the ten-kilogram sample, given the chance. Richard Barrans, Ph.D., M.Ed. Department of Physics and Astronomy University of Wyoming PS I guess i was not very clear in describing my scenario. Internal energy E is basically total energy of the sample. The first law of thermodynamics Delta E = q + w is a conservation of energy statement: the change in internal energy E is equal to the heat added to the system q plus the work done on the system w. So yes, if you have a one-kilogram sample of water and a ten-kilogram sample of water both at the same temperature, the ten-kilogram sample will have more internal energy and can melt more ice cubes (or, in my preferred demonstration, boil more liquid nitrogen). In the scenario I described in my previous response, I was proposing a case in which two samples had different masses but the same internal energy, so the one with the least mass had more energy per mass. More concretely, If you place a hot cup of tea in contact with an iceberg, the tea will transfer heat to the iceberg, even though the iceberg has much greater internal energy due to its much greater mass. Perhaps that would have been a better illustration to begin with. Rich Barrons Hello, Yes, it is possible for heat to flow between two objects with the same internal energy. Heat will flow if there is a temperature different between the two bodies, from the warmer one to the colder one, regardless of internal energies. The relation between temperature and internal is not a simple one. It is complex because internal energy is the sum of a number of forms of energy that molecules in a body have (such as the kinetic energy due to the (translational, rotational, vibrational) motion of molecules, the potential energy of the molecules, the energy in all the chemical bonds, etc.) whereas temperature is related to only one of these energies, namely the translational kinetic energy. So, two bodies can have an identical internal energy but tremendously different temperatures (with heat flowing from the warmer one to the colder one irrespective of their internal energy). Consider, for example, the example of a hot stream of gas passing over cooler water. Water heats up even though liquids, such as water, generally have a lot more internal energy than a gas. Thus, not only heat can flow from two objects with the same internal energy, but also actually heat can flow from one with a lower internal energy to one with higher internal energy. Ali Khounsary, Ph.D. Advanced Photon Source Argonne National Laboratory Click here to return to the Physics Archives

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