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SM-Mod05 Application to Nondegenerate Perfect GasesNode id: 3215page |
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SM-Mod02 Thermodynamics -- Review ProblemsNode id: 3214page |
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SM-Mod01 Probability and Statistics Node id: 3213page |
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SM-Mod03 Microcanonical EnsembleNode id: 3182page |
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SM-Mod04 Canonical Partition FunctionNode id: 3181page |
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test pageNode id: 3054page |
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A list of complete reference to sources of questions and problemsNode id: 2888pageThis page gives an incomplete, but growing list of sources from which many problems have been compiled. Many questions and problems are obvious variations of the original one, an effort is made to list corresponding sources also. Needless to say that this task will never achieve a complete list, neverthelss it has been taken to give the credit where it is due. The users are welcome to leave comments with regard to source on the appropriate problem page. |
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QM-Mod07 Canonical QuantizationNode id: 2800pageThis section has problems on canonical quantization and uncertainty relation. |
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QM-Mod14-15 :: Problems in Two and Three DimensionsNode id: 2766page |
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QM-Mod10 :: Working with representationsNode id: 2761pageThis section has problems on coordinate and momentum representations.
To continue
Click on the Table of Contents at the top;
Alternatively use navigation links at the bottom right. |
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QM-Mod08 :: Using raising and lowering operators Node id: 2729page |
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QM-Mod20 :: Spin and Identical ParticlesNode id: 2676page |
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Problem-EM-02002Node id: 2624pageThree equal charges are placed at the corners of an equilateral triangle.Show that the electric field at the center is zero. |
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CM-Mod04 :: Hamiltonian FormulationNode id: 2553pageThis section hs problems on Hamiltonian formulation ofclassical mechanics. |
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QM-Mod09 :: Time Development and Pictures in Quantum MechanicsNode id: 2517pageProblems and Short Questions on Time Development in QM can be found here. Follow Navigation Links at the Bottom of the page. |
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CM-Mod07 :: S:mall OscillationsNode id: 2347page |
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Problem-SM-04001Node id: 2250pageOnce the canonical partition function is known all properties of a system can be derived. Find the equation of state and the heat capacity of systems for which the partition funcion is (a) \(Z=V^N(2\pi/\beta M)^{5N/2}\); (b) \(Z= (V-Nb)^N (2\pi/\beta M)^{3N/2} e^{\beta N^2/V} \qquad a,b \text{ are constants}\).
Identify the systems. Atlee Jackson* |
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Problem-TH-04002Node id: 2246pageThe molar energy of a monoatomic gas which obeys van der Waal's equation is given by
\( E= \frac{3}{2}kT - \frac{a}{v}\),
where \(V\) is the volume at temperature \(T\), and \(a\) is a constant. Initially one mole of gas is at temperature \(T_1\) and occupies volume \(V_1\). The gas is allowed to expand adiabatically into a vacuum so that it occpies a total volume \(V_2\). What is the final temperature of the gas? MANDL |
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CM-Mod09 Rigid BodyDynamicsNode id: 2206page |
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Problem-TH-03001 Work done; van der Waals gasNode id: 2200pageConsider \(N\) molecules of a gas obeying van der Waals equation of state given by
\[\left(P+ \frac{a N^2}{V^2}\right)\big(V-Nb\big) = Nk_B T\]
where \(a\) is a measure of the attractive forces between the molecules and \(b\) is another constant proportional to the size of a molecule. The other symbols have their usual meanings. Show that during an isothermal expansion (Temperature is kept onstant) from volume \(V_1\) to volume \(V_2\) quasi-statically and reversibly, the work done is
\[ W =-Nk_B T \log\left(\frac{V_2-Nb}{V_1-Nb}\right) + a^2 \Big(\frac{1}{V_1}-\frac{1}{V_2}\Big)\] |
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