(Solved): Thermodynamic Q4 (Final-Course \( 1^{\text {st }} 2016 / 2017 \) ): (a) A system, maintained at co ...

Thermodynamic

Q4 (Final-Course \( 1^{\text {st }} 2016 / 2017 \) ): (a) A system, maintained at constant volume, is brought in contact with a thermal reservoir at temperature \( T_{0} \). If the initial temperature of the system is \( \mathrm{T}_{\mathrm{i}} \), calculate the change in the total entropy of the (system \( + \) reservoir). You may assume that the specific heat of the system, is independent of temperature. (b) Assume now that the change in system temperature is brought about through successive contacts with \( (\mathrm{N}) \) reservoirs at temperature \( \mathrm{T}_{\mathrm{i}}+\Delta \mathrm{T}, \mathrm{T}_{\mathrm{i}}+2 \Delta \mathrm{T}, \ldots, \mathrm{T}_{0}-\Delta \mathrm{T} \), \( T_{0} \), where \( N \cdot \Delta T=\left(T_{0}-T_{i}\right) \). (The figure shows the process at \( \mathrm{n}+1 \) ). Show that in the limit \( N \rightarrow \infty, \Delta \mathrm{T} \rightarrow 0 \) with \( \mathrm{T}_{0}=\mathrm{T}_{\mathrm{i}}+2 \Delta \mathrm{T} \) N. \( \Delta \mathrm{T}=\left(\mathrm{T}_{0}-\mathrm{T}_{\mathrm{i}}\right) \) is fixed the change of the entropy of the system and the entropy of surrounding equals to zero. (c) Comment on the difference between (a) and (b) in the light of the second law of thermodynamics.