Questions 71-73
The internal energy of this system at any temperature T is given by
. The heat capacity of the system is given by which of the following expressions?
A.^2\frac{e^{\epsilon/kT}}{\left&space;(1+e^{\epsilon/kT}&space;\right&space;)^2} "N_0 k \left (\frac{\epsilon}{kT} \right )^2\frac{e^{\epsilon/kT}}{\left (1+e^{\epsilon/kT} \right )^2}")
B.^2\frac{1}{\left&space;(1+e^{\epsilon/kT}&space;\right&space;)^2} "N_0 k \left (\frac{\epsilon}{kT} \right )^2\frac{1}{\left (1+e^{\epsilon/kT} \right )^2}")
C.^2e^{-\epsilon/kT} "N_0 k\left( \frac{\epsilon}{kT} \right )^2e^{-\epsilon/kT}")
D.^2 "\frac{N_0 k}{2} \left (\frac{\epsilon}{kT} \right )^2")
E.
Heat Capacity (at constant volume),_V "C_V=\left (\frac{\partial U}{\partial T} \right )_V")
^2\frac{e^{\epsilon/kT}}{\left&space;(1+e^{\epsilon/kT}&space;\right&space;)^2} "\\U= E_1 N_0+\frac{N_0\epsilon}{1+e^{\epsilon/kT}} \\\\\frac{\partial U}{\partial T}= N_0 k \left (\frac{\epsilon}{kT} \right )^2\frac{e^{\epsilon/kT}}{\left (1+e^{\epsilon/kT} \right )^2}")
Answer: A
A system in thermal equilibrium at temperature T consists of a large number N0 of subsystems, each of which can exist only in two states of energy E1 and E2, where 
. In the expressions that follow, k is the Boltzmann constant.
The internal energy of this system at any temperature T is given by
A.
B.
C.
D.
E.
(GR9277 #72)
Solution:
Heat Capacity (at constant volume),
Answer: A
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