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The diagram below shows a one-dimensional row of 5 microscopic objects each of mass 5 ✕ 10−26 kg, connected by forces that can be modeled by springs of stiffness 30 N/m (so each object can be modeled as if it were connected to a single spring of effective stiffness 4ks = 120 N/m -- neglect any possible differences for objects near the ends). These 5 objects can move only along the x axis.
Calculate the heat capacity per object when the total energy is 4 quanta. (Think of this in terms of increasing from 3.5 quanta of energy in the system to 4.5 quanta of energy in the system, if that were possible.)
If the temperature were raised very high, classically what would we expect the heat capacity per object to be for this one-dimensional system? Give a numerical value.
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