Thermal Properties of Matter - Calorimetry Question with Solution | TestHub

A well insulated box contains water (specific heat $=\mathrm{C}$ and very large conductivity) of mass ${\mathrm{m}}_0$ and temperature ${\mathrm{T}}_0$ at time $\mathrm{t}=0$. If heat is being added to it uniformly at a constant rate $\mathrm{dQ}/\mathrm{dt}=\mathrm{R}$ and water is leaking from it at a constant rate $\frac{\mathrm{dm}}{\mathrm{dt}}=\lambda$ then the temperature of the water at time $\mathrm{t}\left(\mathrm{t}<\frac{{\mathrm{m}}_0}{\lambda }\right)$ will be:-