An object of mass specific heat and temperature is placed

Chapter 20, Problem 20.63

(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.

Text Transcription:

m_1

c_1

T_1

m_2

c_2

T_2 > T_1

Delta S = m_1c_1 ln T/T_1 + m_2c_2 ln T’/T_2

m_1c_1(T - T_1) = m_2c_2(T_2 - T’)

Delta S