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Solved: Determine the total entropy change and exergy
Chapter 13, Problem 91P(choose chapter or problem)
Determine the total entropy change and exergy destruction associated with the process described in Prob. 13–89, using
(a) the ideal-gas approximation and
(b) Kay's rule. Assume constant specific heats and \(T_{0}=30^{\circ} \mathrm{C}\).
Questions & Answers
QUESTION:
Determine the total entropy change and exergy destruction associated with the process described in Prob. 13–89, using
(a) the ideal-gas approximation and
(b) Kay's rule. Assume constant specific heats and \(T_{0}=30^{\circ} \mathrm{C}\).
ANSWER:Step 1 of 11
a)
Write the entropy balance equation to find the expression of entropy generation in terms of \({O_2}\) and \({N_2}\).
\({S_{in}} - {S_{out}} + {S_{gen}} = \Delta {S_{system}}\)
\(\frac{{{Q_{in}}}}{{{T_{b,surr}}}} + {S_{gen}} = m\left( {{s_2} - {s_1}} \right)\)
\({S_{gen}} = m\left( {{s_2} - {s_1}} \right) - \frac{{{Q_{in}}}}{{{T_{surr}}}}\)
\({S_{gen}} = {m_{{O_2}}}{\left( {{s_2} - {s_1}} \right)_{{O_2}}} + {m_{{N_2}}}{\left( {{s_2} - {s_1}} \right)_{{N_2}}} - \frac{{{Q_{in}}}}{{{T_{surr}}}}\;\;\;\;\;...\;\left( 1 \right)\)
Here, mass of \({O_2}\) is \({m_{{O_2}}}\), mass of \({N_2}\) is \({m_{{N_2}}}\), boundary temperature is \({T_{b,surr}}\), surrounding temperature is\( {T_{surr}}\), entropy at state 1 and 2 is \({s_1}\) and \({s_2}\), entropy generation is \({S_{gen}}\), change in entropy of a system is \(\Delta {S_{system}}\), heat input is \({Q_{in}}\), outlet entropy is \({S_{out}}\), and inlet entropy is \({S_{in}}\).
From the Table of ideal gas specific heats of various common gases, obtain the constant pressure specific heats \(\left( {{c_p}} \right)\) of \({O_2}\) and \({N_2}\) at \(210\;{\rm{K}}\) and \(180\;{\rm{K}}\) as,
\({c_{p,{O_2}@210\;{\rm{K}}}} = 0.918\;\frac{{{\rm{kJ}}}}{{{\rm{kg}} \cdot {\rm{K}}}}\)
\({c_{p,{N_2}@180\;{\rm{K}}}} = 1.039\;\frac{{{\rm{kJ}}}}{{{\rm{kg}} \cdot {\rm{K}}}}\)