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183_notes:internal_energy [2014/10/28 19:51] – [Achieving Thermal Equilibrium] caballero | 183_notes:internal_energy [2021/04/15 16:58] – [Systems With Structure Can Have Internal Energy] stumptyl | ||
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+ | Section 7.4 in Matter and Interactions (4th edition) | ||
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===== Internal Energy ===== | ===== Internal Energy ===== | ||
- | Up to now, you have read about systems that have no internal structure: [[183_notes: | + | Up to now, you have read about systems that have no internal structure: [[183_notes: |
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+ | ==== Lecture Video ==== | ||
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+ | {{youtube> | ||
==== Systems With Structure Can Have Internal Energy ==== | ==== Systems With Structure Can Have Internal Energy ==== | ||
- | [{{ 183_notes: | + | [{{183_notes: |
+ | \\ | ||
- | Until now, you have considered systems of point particles, which have no internal structure. You will now relax that condition. | + | __//Until now, you have considered systems of point particles, which have no internal structure. You will now relax in that condition.//__ |
- | Consider two systems of two particles (each of mass $m$) attached by a spring ($k_s$) moving to the left with a speed $v$ (figure to left). For one of the systems, the spring is at it relaxed length. For the other, the spring is compressed by a //massless// string tied around the objects. Which system has more energy? | + | Consider two systems of two particles (each of mass $m$) attached by a spring ($k_s$) moving to the left with a speed $v$ (figure to left). For one of the systems, the spring is at its relaxed length. For the other, the spring is compressed by a massless string tied around the objects. Which system has more energy? |
- | Clearly, both have the same kinetic energy ($K=\dfrac{1}{2} (M) v^2$; $M$ is the total mass of the system). But what about the energy associated with spring compression that is internal to the system? The object with the compressed spring has more //internal energy//. These are the kinds energy distinctions that you will need to make when objects have structure. | + | Clearly, both have the same kinetic energy ($K=\dfrac{1}{2} (M) v^2$; $M$ is the total mass of the system). But what about the energy associated with spring compression that is internal to the system? The object with the compressed spring has more //internal energy//. These are the kinds of energy distinctions that you will need to make when objects have structure. |
- | === Internal | + | ==== Internal |
- | {{ 183_notes: | + | {{ 183_notes: |
- | {{ 183_notes: | + | {{ 183_notes: |
- | You have already seen one form of internal energy (i.e., when a spring is compressed). It can be useful to be able to unpack the different forms of internal energy to work on a particular problem of interest. An object that is rotating about its center of mass will have internal energy associated with rotation: | + | You have already seen one form of internal energy (i.e., when a spring is compressed). It can be useful to be able to unpack the different forms of internal energy to work on a particular problem of interest. An object that is rotating about its center of mass will have internal energy associated with rotation: |
- | As you read previously, the total mass of the system is related to the system' | + | As you [[183_notes: |
The total internal energy of a system is given by the sum of all the possible forms of internal energy that the system can have, | The total internal energy of a system is given by the sum of all the possible forms of internal energy that the system can have, | ||
$$\mathrm{Internal\: | $$\mathrm{Internal\: | ||
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==== Thermal Energy is due to Random Motion ==== | ==== Thermal Energy is due to Random Motion ==== | ||
- | In this section, we will focus on thermal energy. You have modeled atoms in a solid as single particles | + | In this section, we will focus on thermal energy. You have [[183_notes: |
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+ | Thermal energy is associated with random motion of the atoms in the solid and is not recognized as collective behavior. It is distinct from the rotation and vibration of atoms as well. This random component of the internal energy is thermal and we associate it with the temperature of the solid. The higher the thermal energy of a particular solid, the more the atoms //jiggle// randomly, and the higher the temperature of that solid.((In fact, the temperature is related to both the energy and the [[http:// | ||
+ | ==== Lecture Video ==== | ||
+ | |||
+ | {{youtube> | ||
- | Thermal energy is associated with random motion of the atoms in the solid and is not recognized as collective behavior. It is distinct form the rotation and vibration of atoms as well. This random component of the internal energy is thermal and we associate it with the temperature of the solid. The higher the thermal energy of a particular solid, the more the atoms //jiggle// randomly, and the higher the temperature of that solid.((In fact, the temperature is related to both the energy and the [[http:// | ||
==== Quantifying Thermal Energy using Temperature ==== | ==== Quantifying Thermal Energy using Temperature ==== | ||
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In the 1800s, [[http:// | In the 1800s, [[http:// | ||
- | He discovered that it required 4.2 J to raise the temperature of a single gram of water by 1 Kelvin (1 K). Thus, the //heat capacity// of an object is the amount of energy needed to raise its temperature by 1 Kelvin. The //specific heat capacity// is a property of the material. It is the amount of energy needed to raise 1 gram of the material by 1 Kelvin. For example, the specific heat capacity of water (as measured by Joule) is 4.2 J per gram per Kelvin (4.2 J/K/g)). For other materials, their specific heat capacities are different (e.g., 2.4 J/K/g for ethanol and 0.4 J/K/g for copper). Water has a very large specific heat capacity, so it requires a lot of energy to change | + | He discovered that it required 4.2 J to raise the temperature of a single gram of water by 1 Kelvin (1 K). This lead to the idea of //heat capacity//. The heat capacity |
The relationship between the thermal energy change of a material ($\Delta E_{thermal}$), | The relationship between the thermal energy change of a material ($\Delta E_{thermal}$), | ||
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==== Achieving Thermal Equilibrium ==== | ==== Achieving Thermal Equilibrium ==== | ||
- | Two objects that are in contact but have different temperatures will eventually come to have the same temperature. This equilibration occurs as the higher temperature object transfers thermal energy through microscopic collisions at the interface between the two objects, which propagate through atoms of the lower temperature object. This microscopic work done on the atoms in the lower temperature object is called //heat//. Eventually, atoms in both objects on average are // | + | Two objects that are in contact but have different temperatures will eventually come to have the same temperature. This equilibration occurs as the higher temperature object transfers thermal energy through microscopic collisions at the interface between the two objects. These atoms at the interface collide with atoms further embedded in the lower temperature material and continue to propagate through |
Macroscopically, | Macroscopically, |