Answer
$ \Delta S_{\mathrm{R}-134 \mathrm{a}}=0.0008$
$\Delta S_{\text {chips }}=−0.000687kJ/K$
$\Delta S_{\text {total }}=0.000154kJJ/K$
Work Step by Step
(a) The energy balance for this system can be expressed as
$
\begin{aligned}
\underbrace{E_{\text {in }}-E_{\text {out }}}_{\begin{array}{c}
\text { Net energy trnsfer } \\
\text { by heat, wonk, and mass }
\end{array}} & =\underbrace{\Delta E_{\text {system }}}_{\begin{array}{c}
\text { Changan intemal, kinetic, } \\
\text { potential,etc. energies }
\end{array}} \\
0 & =\Delta U\\
&=\left[m\left(u_2-u_1\right)\right]_{\text {chips }}+\left[m\left(u_2-u_1\right)\right]_{\mathrm{R}-134 \mathrm{a}} \\
{\left[m\left(u_1-u_2\right)\right]_{\text {chips }} } & =\left[m\left(u_2-u_1\right)\right]_{\mathrm{R}-134 \mathrm{a}}
\end{aligned}
$
We determine the heat released by the chips
$
Q_{\text {chips }}=m c\left(T_1-T_2\right)=(0.010 \mathrm{~kg})(0.3 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K})[20-(-40)] \mathrm{K}=0.18 \mathrm{~kJ}
$
The mass of the refrigerant vaporized during this heat exchange process is
$
m_{\mathrm{g}, 2}=\frac{Q_{\mathrm{R}-134 \mathrm{a}}}{u_{\mathrm{g}}-u_f}=\frac{Q_{\mathrm{R}-134 \mathrm{a}}}{u_{f g @-40^{\circ} \mathrm{C}}}=\frac{0.18 \mathrm{~kJ}}{207.40 \mathrm{~kJ} / \mathrm{kg}}=0.0008679 \mathrm{~kg}
$
There is only a small fraction of R-134a which s vaporized during the process. Therefore, the temperature of $R-134a$ remains constant during the process. The change in the entropy of the R-134a is (at $-40^{\circ} \mathrm{F}$ from Table A-$11$)
$
\begin{aligned}
& \Delta S_{\mathrm{R}-134 \mathrm{a}}=m_{g, 2} s_{g, 2}+m_{f, 2} s_{f, 2}-m_{f, 1} s_{f, 1} \\
& =(0.0008679)(0.96866)+(0.005-0.0008679)(0)-(0.005)(0) \\
& =0.00084 \mathrm{~kJ} / \mathrm{K} \\
&
\end{aligned}
$
(b) We calculate the entropy change of the chips:
$
\Delta S_{\text {chips }}=m c \ln \frac{T_2}{T_1}=(0.010 \mathrm{~kg})(0.3 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}) \ln \frac{(-40+273) \mathrm{K}}{(20+273) \mathrm{K}}=-\mathbf{0 . 0 0 0 6 8 7 k J / K}
$
(c) The total entropy change is
$
\Delta S_{\text {total }}=S_{\text {gen }}=\Delta S_{\mathrm{R}-134 \mathrm{a}}+\Delta S_{\text {chips }}=0.000841+(-0.000687)=\mathbf{0 . 0 0 0 1 5 4 k J} \mathbf{J} / \mathbf{K}
$
The positive result for the total entropy change (i.e., entropy generation) indicates that this process is possible.
