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Consider a counter-flow heat exchanger with the inlet temperatures of two fluids $(1$ and $2)$ being $T_1$, in $=300 \mathrm{~K}$ and $T_2$, in $=350 \mathrm{~K}$. The heat capacity rates of the two fluids are $\mathrm{C}_1=1000 \mathrm{~W} / \mathrm{K}$ and $\mathrm{C}_2=400 \mathrm{~W} / \mathrm{K}$, and the effectiveness of the heat exchanger is $0.5.$ The actual heat transfer rate is _________ $\mathrm{kW}$.
 

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