Question #42520

A battery of electromotive force $E = 20 \text{ V}$ and internal resistance $r = 2 \ \Omega$ is connected across a heating coil placed in a calorimeter. The resistance of the coil varies with the temperature elevation $\Delta T$ above the surroundings as $R(\Delta T) = R_0(1 + \alpha \Delta T)$, where $R_0 = 2 \ \Omega$ and $\alpha = 0.05 \text{ K}^{-1}$. The calorimeter loses heat to the surroundings at a rate $P_{\text{loss}} = k \Delta T$, where $k = \frac{15}{16} \text{ W/K}$. Assuming the surroundings are at a constant temperature, what is the steady-state temperature elevation $\Delta T$ of the calorimeter?