Differences

This shows you the differences between two versions of the page.

--- 183_notes:internal_energy [2018/05/29 21:42] – hallstein
+++ 183_notes:internal_energy [2021/06/02 22:49] (current) – [Internal Energy Can Take Different Forms] stumptyl
@@ Line 3: / Line 3: @@
 ===== Internal Energy =====
-Up to now, you have read about systems that have no internal structure: [[183_notes:point_particle|point particle systems]]. Even when considering a [[183_notes:energy_cons#multi-particle_systems|multi-particle system]], you have worked with uniquely identifiable objects. Now, you will read about the energy associated with systems that have some structure. Here, you will read about the connection between [[183_notes:define_energy|the concept of energy]] to [[183_notes:model_of_solids|the ball and spring model of the solid]]. This leads to the concept of thermal energy and how thermal energy is transferred into and out of systems.
+Up to now, you have read about systems that have no internal structure: [[183_notes:point_particle|point particle systems]]. Even when considering a [[183_notes:energy_cons#multi-particle_systems|multi-particle system]], you have worked with uniquely identifiable objects. Now, you will read about the energy associated with systems that have some structure. **In these notes, you will read about the connection between [[183_notes:define_energy|the concept of energy]] to [[183_notes:model_of_solids|the ball and spring model of the solid]].** This leads to the concept of thermal energy and how thermal energy is transferred into and out of systems.
 ==== Lecture Video ====
@@ Line 11: / Line 11: @@
 ==== Systems With Structure Can Have Internal Energy ====
-[{{183_notes:mi3e_07-020.png?150|Two systems with different internal energies, but identical kinetic energies. }}]
+[{{183_notes:week10_internalenergy1.png?150|Two systems with different internal energies, but identical kinetic energies. }}]
+\\
-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 its 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 energy can take different forms ===
+==== Internal Energy Can Take Different Forms ====
-{{ 183_notes:mi3e_07-021.png?150}}
+{{ 183_notes:week10_internalenergy2.png?150}}
-{{ 183_notes:mi3e_07-022.png?250}}
+{{ 183_notes:week10_internalenergy3.png?250}}
-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: //rotational energy//. While an object that is oscillating with respect to its center of mass will have energy due to vibrations: //vibrational energy//. When you eat food, you increase your internal energy in the form of //chemical energy//. A system whose temperature increases will increase its //thermal energy//.
+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: **rotational energy**. While an object that is oscillating with respect to its center of mass will have energy due to vibrations: **vibrational energy**. When you eat food, you increase your internal energy in the form of **chemical energy**. A system whose temperature increases will increase its **thermal energy**.
 As you [[183_notes:point_particle|read previously]], the total mass of the system is related to the system's total energy ($M_{sys} = E_{sys}/c^2$). This indicates that systems with more internal energy will have more mass. However, from a practical standpoint, the enormous rest mass energy associated with macroscopic system overshadows these contributions to the total energy meaning it only makes sense to worry about changes in internal energy whether they be rotational, vibrational, thermal, et cetera.
@@ Line 40: / Line 41: @@
 {{youtube>J__LrHm2-6g?large}}
-==== Quantifying Thermal Energy using Temperature ====
+==== Quantifying Thermal Energy Using Temperature ====
 /* Left out part about thermometers */
@@ Line 48: / Line 49: @@
 In the 1800s, [[http://en.wikipedia.org/wiki/James_Prescott_Joule|James Joule]] connected energy with temperature in [[http://en.wikipedia.org/wiki/James_Prescott_Joule#The_mechanical_equivalent_of_heat|his famous paddle wheel experiment]]. In his experiment, a rotating paddle wheel submerged in water was connected to a falling mass. Joule was able to measure the gravitational potential energy change associated with the falling mass and the temperature change of the water.
-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 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 its temperature.
+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 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 its temperature.
 The relationship between the thermal energy change of a material ($\Delta E_{thermal}$), the specific heat capacity ($C$), and the temperature change ($\Delta T$) is given by,