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Solved: CALC An object of mass m1, specific heat c1, and
Chapter 20, Problem 63P(choose chapter or problem)
An object of mass \(m_1\), specific heat \(c_1\), and temperature \(T_1\) is placed in contact with a second object of mass \(m_2\), specific heat \(c_2\), and temperature \(T_{2}>T_{1}\). As a result, the temperature of the first object increases to T and the temperature of the second object decreases to T’.
(a) Show that the entropy increase of the system is
\(\Delta S=m_{1} c_{1} \ln \frac{T}{T_{1}}+m_{2} c_{2} \ln \frac{T^{\prime}}{T_{2}}\)
and show that energy conservation requires that
\(m_{1} c_{1}\left(T-T_{1}\right)=m_{2} c_{2}\left(T_{2}-T^{\prime}\right)\)
(b) Show that the entropy change \(\Delta S\), considered as a function of T, is a maximum if T = T’, which is just the condition of thermodynamic equilibrium.
(c) Discuss the result of part (b) in terms of the idea of entropy as a measure of disorder.
Questions & Answers
QUESTION:
An object of mass \(m_1\), specific heat \(c_1\), and temperature \(T_1\) is placed in contact with a second object of mass \(m_2\), specific heat \(c_2\), and temperature \(T_{2}>T_{1}\). As a result, the temperature of the first object increases to T and the temperature of the second object decreases to T’.
(a) Show that the entropy increase of the system is
\(\Delta S=m_{1} c_{1} \ln \frac{T}{T_{1}}+m_{2} c_{2} \ln \frac{T^{\prime}}{T_{2}}\)
and show that energy conservation requires that
\(m_{1} c_{1}\left(T-T_{1}\right)=m_{2} c_{2}\left(T_{2}-T^{\prime}\right)\)
(b) Show that the entropy change \(\Delta S\), considered as a function of T, is a maximum if T = T’, which is just the condition of thermodynamic equilibrium.
(c) Discuss the result of part (b) in terms of the idea of entropy as a measure of disorder.
ANSWER:Solution 63P
Step 1
