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Quantum statistical mechanics: Return of the simple harmonic oscillator
The energy levels of a quantum SHO are given by
1. Calculate the QM partition function.
2. Calculate the probability that a measurement of the energy will find the QM SHO in the n-th eigenstate.
3. Calculate the average energy.
4. Calculate the specific heat.
5. Calculate the high-temperature limit of the specific heat.
6. Calculate the leading term in a low-temperature expansion of the specific heat. (You should be able to figure out what a good quantity to expand in would be.)
a full-revolution press has 100 rpm flywheel rotation. the press is equipped with two-hand palm buttons mounted on the
1. Answer the following true or false. (a) A process that violates the second law of thermodynamics violates the first law of thermodynamics.
A thin 100 cm long and 10 cm wide horizontal plate is maintained at a uniform temperature of 150oC in a large tank full of water at 75oC.
If the heater is activated from an initial temperature of 27°C, estimate the time required for the surface temperature to come within 10°C of its steady-state value.
A cantilever beam has been constructed from a steel having Young's modulus E = 208 GPa,Poisson ratio ? = 0.29, and tensile yield strength sy = 410 MPa. The length of the beam, from its base to its tip, is L = 1 m, and the uniform crosssection is rec..
An incompressible ?uid ?ows radially (no y- or f-component) into a small circular drain. How must the radial component of velocity vary with radius as demanded by continuity?
Calculate the change of entropy and the heat supplied. Sketch the process on a T-, diagram. Take the isentropic index. y, for nitrogen as 1.4, and assume that nitrogen is a perfect gas. (0.001 25 kJ/K; 0.407 kJ)
a compressor is used to bring saturated water vapor at 150 lbfin2 up to 2500 lbfin2 where the actual exit temperature
1) Display to the user the purpose of this program 2) In this program you will be converting temperature entered by the user in degree Fahrenheit to a) Degree Celsius b) Degree Kelvin c) Rankine or d) Réaumur 3
a sphere 1 ft in diameter is moving horizontally at a depth of 12ft below water surface where the water temperature is
The efficiency of a refrigerator is given by the coefficient of performance (COP). Write two different expressions for the COP of a refrigeration cycle; one in terms of heat transfer and work input, and the other in terms of heat transfers only.
The engine speed is 2000 rpm clockwise when viewed from the rear. Determine the gyroscopic couple on the aircraft and state its effect. In what way is the effect changed when the (i) aeroplane turns towards right (ii) engine rotates clockwise when..
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