An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of \(95^{\circ} \mathrm{C}\), while the battery and lead wires remain at the ambient temperature of \(25^{\circ} \mathrm{C}\). Neglect the electrical resistance of the lead wires.

(a) Consider the resistor as a system about which a control surface is placed and Equation 1.12c is applied. Determine the corresponding values of \(\dot{E}_{\text {in }}(\mathrm{W}), \dot{E}_{g}(\mathrm{~W}), \dot{E}_{\text {out }}(\mathrm{W})\), and \(\dot{E}_{\text {st }}(\mathrm{W})\). If a control surface is placed about the entire system, what are the values of \(\dot{E}_{\text {in }}, \dot{E}_{g}, \dot{E}_{\text {out }}\), and \(\dot{E}_{\text {st }}\) ?

(b) If electrical energy is dissipated uniformly within the resistor, which is a cylinder of diameter \(D=60\) \(\mathrm{mm}\) and length \(L=250 \mathrm{~mm}\), what is the volumetric heat generation rate, \(\dot{q}\left(\mathrm{~W} / \mathrm{m}^{3}\right)\) ?

(c) Neglecting radiation from the resistor, what is the convection coefficient?

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Battery O 1=6 A V = 24 V Resistor Air T-25C Lead wire