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# particle model liquid

Since the Lennard-Jones potential mimics the spring-mass potential at least for small oscillations, we will assume that this interaction when averaged over time will also result in $$KE_{avg}=PE_{avg}$$. Calculate the heat capacity Cv for this substance assuming all modes are active. 4. Rotational modes typically have lower energy than vibrational modes. In this section we will attempt to make the same connection for thermal energy. One mole of a solid will have $$6N_A$$ number of modes, resulting in a total thermal energy of: How many modes do different gases have? Watch the recordings here on Youtube! Specifically, we would like to develop an understanding of heat capacity from Chapter 1 in terms of microscopic parameters. In the previous section we said that macroscopic bond energy can be modeled as the sum of pair-wise potential energies between all pairs at their equilibrium configurations (at zero temperature). They interpret diagrams on cards showing representations of particles and may observe a teacher demonstration. 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. The activities are designed to help students order their thoughts, with discussion and questions playing a part. The table below shows heat capacity patterns that are seen in different gases. Using tools of statistical mechanics (which is beyond the scope of this course) it can be shown that each type of energy that a substance can have, or each mode, has this amount of thermal energy: $E_{\text{thermal}}(\text {per mode}) = \frac{1}{2}k_{B}T$. Setting the two equations equal to each other, using the gas constant $$R=N_Ak_B=8.314 \frac{J}{Kmol}$$, and solving for molar heat capacity $$c_{v,mol}$$ ($$C_V=c_{v,mol}$$ for one mole or NA number of particles), we get: $c_{v,mol}=\frac{R}{2}\text{(# modes per particle)}\label{Cv}$. 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. 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. Thus, Cy atoms are on average moving three times faster than Ai atoms. Four to five samples gases – ideally two should be coloured, eg chlorine (FLAMMABLE and CORROSIVE) or bromine (TOXIC and CORROSIVE depending on concentration), Mini whiteboards, enough for each student. If you teach primary science, see the guidance below to find out how to use this resource.

Classify substances as elements, compounds, mixtures, metals, non-metals, solids, liquids, gases and solutions.