The temperature of a liquid stream in a heat exchanger is determined by thermocouples as shown in Figure P13.20. One thermocouple is attached to the tube wall and it measures a temperature of \(300 \mathrm{~K}\). The second thermocouple is soldered to the wall of a steel thermocouple well and it records a temperature of \(350 \mathrm{~K}\). The thermocouple well is \(0.05 \mathrm{~m}\) long with an inner and outer diameter of 5 and \(12.5 \mathrm{~mm}\) respectively. The water is flowing at a rate of \(1 \mathrm{~m} / \mathrm{min}\). Determine the temperature of the water, \(T_{\infty}\), at the point where the thermocouple is attached to the well.

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FIGURE P13.20 Water Th 00 L d do Steel ks