Thermodynamics: An Engineering Approach 8th Edition

Published by McGraw-Hill Education
ISBN 10: 0-07339-817-9
ISBN 13: 978-0-07339-817-4

Chapter 10 - Vapor and Combined Power Cycles - Problems - Page 591: 10-14

Answer

$ \eta_{\text {th }}=0.375$

Work Step by Step

From the steam tables (Tables A-4, A-5, and A-6), $$ \begin{aligned} & P_1=P_{\text {sat } @ 40^\circ \mathrm{C}}=7385\ \mathrm{kPa} \\ & P_2=P_{\text {sat } @ 300^\circ \mathrm{C}}=8588\ \mathrm{kPa} \\ & h_1=h_{f @ 40^\circ \mathrm{C}}=167.53 \mathrm{~kJ} / \mathrm{kg} \\ & v_1=v_{f @ 40^{\circ} \mathrm{C}}=0.001008 \mathrm{~m}^3 / \mathrm{kg} \\ & w_{\mathrm{p}, \text { in }}=\boldsymbol{v}_1\left(P_2-P_1\right) \\ & \begin{array}{l} =\left(0.001008 \mathrm{~m}^3 / \mathrm{kg}\right)(8588-7.385) \mathrm{kPa}\left(\frac{1 \mathrm{~kJ}}{1 \mathrm{kPa} \cdot \mathrm{m}^3}\right) \\ =8.65 \mathrm{~kJ} / \mathrm{kg} \end{array} \\ & =8.65 \mathrm{~kJ} / \mathrm{kg} \\ & h_2=h_1+w_{\text {p,in }}=167.53+8.65=176.18 \mathrm{~kJ} / \mathrm{kg} \\ & \left.\begin{array}{l} T_3=300^{\circ} \mathrm{C} \\ x_3=1 \end{array}\right\} \begin{array}{l} h_3=2749.6 \mathrm{~kJ} / \mathrm{kg} \\ s_3=5.7059 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K} \end{array} \\ & \left.\begin{array}{l} T_4=40^{\circ} \mathrm{C} \\ s_4=s_3 \end{array}\right\} \begin{array}{l} x_4=\frac{s_4-s_f}{s_{f g}}=\frac{5.7059-0.5724}{7.6832}=0.6681 \\ h_4=h_f+x_4 h_{f g}=167.53+(0.6681)(2406.0)\\=1775\text{ kJ/kg} \end{array} \end{aligned} $$ Thus, $$ \begin{aligned} w_{\mathrm{T}, \text { out }} & =h_3-h_4=2749.6-1775.1=\mathbf{9 7 4 . 5}\ \mathbf{k J} / \mathbf{k g} \\ q_{\text {in }} & =h_3-h_2=2749.6-176.18=\mathbf{2 5 7 3 . 4 ~k J} / \mathbf{k g} \\ q_{\text {out }} & =h_4-h_1=1775.1-167.53=1607.6\ \mathrm{~kJ} / \mathbf{k g} \end{aligned} $$ The thermal efficiency of the cycle is $$ \eta_{\text {th }}=1-\frac{q_{\text {out }}}{q_{\text {in }}}=1-\frac{1607.6}{2573.4}=\mathbf{0 . 3 7 5} $$
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