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In quantum mechanics we learn that the average energy of a simple harmonic oscillator is given by ε = (n + 1/2) hω, with n = 0, 1, 2,... Classically, the energy is given by ε = (1/2m)p2x + (1/2)κx2.
(a) What would be the classical value of the heat capacity for N of these oscillators? (Use equipartition.)
(b) If the heat capacity fell well below the classical value for temperatures below 190 K, what would you estimate the frequency ω to be?
(c) In real solids having Na atoms, we might expect 6Na degrees of freedom, each with an average energy (1/2)kT , giving a total thermal energy of 3NakT . But at temperatures below the Debye temperature, the internal energy is lower than this. Does this violate the equipartition theorem? Explain.
Critical evaluation and comments by the student on the usefulness of the training and its relevance to university education, Safety and environmental procedures adhered to within the industry.
Note in Figs. 10.10 and 10.11 that the minimum energy loss for a gradual contraction (K = 0.04 approximately) occurs when the cone angle is in the range of 15° to 40°. Make scale drawings of contractions at both of these extremes for a reduction f..
A machine of mass 400 kg operates at 1500 rpm and has an unbalanced which causes a harmonic repeated force pf magnitude 20,000 N. Design an isolation system to limit the transmitted force to 3,500 N and the amplitude of vibration during operation to ..
a vertical piston-cylinder device initially contains 0.25 m3 of air at 600 kpa and 300degc. a valve connected to the
Because of its very low spring constant, the spring is assumed to apply a constant force of 25 N. Determine the maximum speed of the cam so that the follower does not lose contact with the cam.
1. calculate the percent of the total resistance for external diffusion internal diffusion and surface reaction.2.
an adiabatic control volume with steam as the working fluid operates at steady flow conditions with the inlet state of
Heat is to be removed from a reaction vessel operating at 75°C by supplying water at 27°C and 0.12 kg/s through a thin-walled tube of 15-mm diameter. The convection coefficient between the tube outer surface and the fluid in the vessel is 3000 W/m..
Neglect the effect of flow rate on F′. The collector has a heat loss conductance of 4 W/m2°C.
a storage tank is 40 feet above a river. water is pumped from the river to the storage tank at a rate of 0.095m3s. the
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read the titled books drilling fluid engineering manual. textbook prepared by m-i drilling fluids co.1998 halliburton
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