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Use Table 3.1 to compute the temperatures of solid A and
Chapter 3, Problem 1P(choose chapter or problem)
Use Table 3.1 to compute the temperatures of solid A and solid B when \(q_{A}=1\). Then compute both temperatures when \(q_{A}=60\). Express your answers in terms of \(\epsilon / k\), and then in kelvins assuming that \(\epsilon=0.1 \mathrm{eV}\).
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QUESTION:
Use Table 3.1 to compute the temperatures of solid A and solid B when \(q_{A}=1\). Then compute both temperatures when \(q_{A}=60\). Express your answers in terms of \(\epsilon / k\), and then in kelvins assuming that \(\epsilon=0.1 \mathrm{eV}\).
ANSWER:Step 1 of 3
The temperature of the system is the reciprocal of entropy and its volume \(\left( V \right) \)and number of particles \(\left( N \right) \)are held fixed. The mathematical expression is,
\(T = {\left( {\frac{{\Delta U}}{{\Delta S}}} \right)_{N,{\rm{ }}V}}\;\;\;\;\;...........(1) \)
The total entropy is equal to the sum of the entropies of the two systems, A and B if they are in thermal equilibrium. Considering the entropies of the system as follows: \({{\rm{S}}_{\rm{A}}},{{\rm{S}}_{\rm{B}}}\) and \(S_{total}\).
At the equilibrium,
\(\frac{{\partial {S_A}}}{{\partial {U_A}}} = \frac{{\partial {S_B}}}{{\partial {U_B}}}\)
At equilibrium, overall entropy is highest.
If compared to two lines in the table for \({q_A} = 11\) and \({q_B} = 13\) as given. Consider the middle of the small interval. That indicates the temperature at \({q_A} = 12\) is considered.
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