In words the above equation means that temperature is a measure of the average energy in an active mode when the sample is in thermal equilibrium. Mini whiteboards might be used by students to sketch the particle pictures before committing these to paper. Generally, a polyatomic gas is composed of molecules having N number of atoms. There is a name, or label, for “way to have energy", which we call a mode, also sometimes referred to as a degree of freedom. which pile represents solids, which liquids and which gases. Share the objectives with the students and explain that they will look at modelling to describe gases, liquids and solids, and to explain differences in their properties. Setting the two kinetic energies equal to each other: \[\frac{1}{2}m_{Ai}v_{Ai}^2=\frac{1}{2}m_{Cy}v_{Cy}^2\nonumber\], \[\frac{v_{Cy}^2}{v_{Ai}^2}=\frac{m_{Ai}}{m_{Cy}}=9\nonumber\]. The three states of matter are solid, liquid and gas. Since most vibrating systems can be described by a spring like potential, we will model these oscillating particles as a masses held in place by three perpendicular springs, one for each independent spacial dimension, as depicted in the figure below. In order to make sense of how thermal energy can be formulated from these random fluctuations, we would like to know how many ways does each of these particles can “have energy” and how is the total energy distributed among these different "ways"? If you teach primary science, see the guidance below to find out how to use this resource. The table below shows heat capacity patterns that are seen in different gases. Non-linear molecules, such as H2O, are not symmetric can rotate around all 3 axes, thus have 3 KErot modes. The total number modes is the number of particles times the number of modes per particle, so for the solid we get: \[\text{total # modes} = 10N_A\times 6 = 60N_A\nonumber\], \[\text{total # modes} = 60N_A = 12N_A\text{( # modes per particle)}\nonumber\]. But we need to be careful that we are actually comparing the same things. It is the responsibility of the teacher to carry out appropriate risk assessments for the demonstrations. In Chapter 1 for pure substances in the temperature range where the Three-Phase Model is valid we said that the total energy of a system is given by: In the microscopic description of particles interacting with the Lennard-Jones potential the total energy of a system is: \[E_{tot}=PE_{tot}+KE_{tot}\label{Etot2}\]. Missed the LibreFest? All linear molecules have 3 KEtrans modes and 2 KErot. Translational modes are always active, as long as the temperature is above zero Kelvin. 2. When this happens, we say that mode is frozen out. [ "article:topic", "authorname:ucd7", "license:ccby", "showtoc:no" ]. b) You add enough energy to break all weaker bonds. The activity provides an opportunity for students to: Reinforce their understanding of the terms gas, liquid and solid. Investigate the reaction of sodium with chlorine, using students’ understanding of atoms, ions and lattice structure, in this lesson plan for 14–16 year olds. As shown in the figure these are rotations about the y- and z- axes. Legal. Peer advocacy acts as a further stimulus to encourage learning and understanding. Thus, the solid will have a larger temperature change. Figure 3.5.4: Heat Capacity as a function for temperature for various gases. Examine data relating to the structure and complexity of compounds, including mass, infrared and NMR spectra, in this workshop lesson plan for 16–18 year olds. Figure 3.5.2: Modes in a diatomic molecule. Since \(c_{v,mol}/R=\text{(# modes per particle)}/2\), the plot is showing us how the number of modes per particle changes with temperature. 3. For example, we see that around room temperature diatomic molecules have 5 modes, instead of the possible 7 modes, implying that the two vibrational modes are inactive. Let us now make the connection between the definition of macroscopic thermal energy from Chapter 1 and the microscopic description presented here. Students think about gases, liquids and solids in terms of the particle model. 2) In another experiment you combine 2 moles of a solid with 3 moles of a diatomic gas with vibrational modes frozen in an insulated contained. If the mass of Ai is nine times the mass of Cy, calculate the ratio of their speeds at T=500K. Give each pair a full set of Particle cards. This data tells us that not all modes are active at all temperature. A molecule is linear, when all atoms are arranged in a straight line, such as all diatomic molecules. There is further information about safety on the demonstration sheet. Figure 3.5.1: Model of thermal energy with particles attached to springs. The important point to remember here, is that regardless of the actual kind of chemical bonding (types of bonds and the geometrical configuration of the bonds) the thermal energy due to the oscillation of the atoms or molecules (treated as rigid particles) is modeled as if they are connected by three independent springs, corresponding to the three independent spatial dimensions in a 3-D universe. The potential and kinetic energies that are associated with those oscillations can each be divided into three independent terms, each one corresponding to one of the three independent spatial dimensions. Each type of gas, e.g., monatomic, has similar values of specific heats, and the values are ordered from smaller to larger as we go from monatomic to diatomic to triatomic, as implied by Equation \ref{Cv}. Describe and model the structure of the atom in terms of the nucleus, protons, neutrons and electrons; comparing mass and charge of protons neutrond and electrons. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Agree with the students the criteria that will be used to assess their responses and explain how the assessment will be made. Display four to five samples of a solid, four to five samples of a liquid, and four to five samples of a gas (ideally two should be coloured, eg chlorine or bromine). where \(k_{B}=1.38\times10^{-23} J/K\) is the Boltzmann constant and T is temperature. In a simple monatomic gas, composed of single atoms, such as He or Ne gases, aka Noble gases, the atoms are no longer interacting with a pair-wise potential since their average separations are \(r\sim 10\sigma\). Give each student a copy of the ‘Gases, liquids and solids’ worksheet. There is further information about safety on the demonstration sheet. When students have completed their sheets, ask them to: Purpose and criteria for successful outcomes of the work are made explicit so that students are clear about what they are doing. Particles not close together and randomly organised. Since there are 4NA total atoms, there will be 2NA AiCy molecules. d) You take two moles of the substance in part a) and one mole of the substance in part b) and place them together in an insulated container. Thus, Cy atoms are on average moving three times faster than Ai atoms. Invite students to describe what they see. Substances are made up of tiny particles. Heat capacity: \[C_v = nc_{v,mol} = 2\times 7\times \frac{R}{2} = 58.2 J/K\nonumber\]. The figure below shows the constant volume molar heat capacity, scaled with gas constant, for several gases from room temperature up to several thousand kelvin. When students have completed their sheets, ask them to: Act as advocate for their partner’s success. We have simple expression above that connects the idea of heat capacity that can be experimentally measured in a lab using macroscopic substances with the microscopic idea of each particle in a substance having an energy mode. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. 4. As we previously discussed at lower temperature some modes get frozen out when there is not enough energy to overcome the quantum energy gap to excite a particular mode. Rather the atoms are moving around freely in three-dimensions. In the Particle Model of Thermal Energy we describe thermal energy of a macroscopic solid of liquid in terms of random fluctuations of subatomic particles which vibrate in the three spacial dimensions. Therefore, each particle in a liquid or solid has at least these six independent ways it can "have energy". The concept must be approached with real caution so students are helped to make the link between the concrete substance and the abstract particle. 1) You perform various experiments to determine properties of an unknown substance. Calculate the heat capacity Cv for this substance assuming all modes are active. Asking their own questions about scientific phenomena. The differences between solids, liquids and gases in terms of particle distribution. Particle Model of Thermal Energy. The activities are designed to help students order their thoughts, with discussion and questions playing a part. Particles close to one another and neatly ordered. Different substances are made of different particles. When we asked how many ways does each spring in a solid can have energy, the answer was two, one kinetic and one potential. Thus: \[KE_{avg}=\frac{1}{2}mv_{avg}^2=\frac{3}{2}k_BT\]. Therefore, we specify that the sample be kept at constant volume during the heat capacity measurement. That is, there will be about as much energy associated with the random energies of a small piece of the sample as in any other same size small piece. Arrange students to work in pairs. In addition, as for the monatomic gas, the molecule as a whole is free to move in space, since it is not interacting with other molecules. The solid has \(2N_A\times 6=12N_A\) total number of modes, and the diatomic gas with vibrational modes frozen out has \(3N_A\times 5=15N_A\) total number of modes. In Section 2.6 we discussed that averaged over time the kinetic and potential energies are the same for a spring-mass system, and as a result half of the total energy. Particle models: gas, liquid, solid: 11-14: Students think about gases, liquids and solids in terms of the particle model. Each particle is free to move in one-dimension only. Each type of gas, e.g., monatomic, has similar values of specific heats, and the values are ordered from smaller to larger as we go from monatomic to diatomic to triatomic, as implied by Equation \ref{Cv}. For a diatomic molecule only two rotational modes are energetically allowed (for quantum mechanical reasons we will not address here). Since there are three dimensions, each atom in a monatomic gas will have 3 modes. what they think ‘neatly ordered’ and ‘randomly organised’ mean. Purpose and criteria for successful outcomes of the work are made explicit so that students are clear about what they are doing. If we add some energy to the two-particle system without breaking the bond, the bond energy does not change, so only thermal energy changes. mension, as depicted in the figure below. Our next task to to count the number of modes per particle for different types of substances. As energy is added to the system increasing thermal energy only, the range of fluctuations increasing, which increases both the average potential and kinetic energy, as can be viewed on the figure below. c) Ai and Cy atoms are at the same temperature, thus they’ll have the same \(KE= \frac{3}{2}k_BT =\frac{1}{2}mv^2\). The important point here is that we have a way to directly measure the change in the thermal energy by measuring the heat capacity of a sample at constant volume, ensuring all the heat we put into the sample goes to changing its thermal energy and not doing some work by expanding the container or pushing against the air in the room. The double lines represent strong Ai-Cy bonds, where the single lines are weaker AiCy-AiCy bonds.


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