A room is $7\mathrm{m}$ by $5\mathrm{m}$ by $3\mathrm{m}$ and the walls are of brick $20\mathrm{cm}$ thick and have windows of glass $0.05\mathrm{cm}$ thick and of total area $5{\mathrm{m}}^2$. The temperature of the room is $20°\mathrm{C}$ higher than that outside. Calculate approximately the quantity of heat that is passing out per minute through the wall and the windows of the room. The thermal conductivity of brick and glass may be taken as $12\times {10}^{-4}$ and $17\times {10}^{-4}$ c.g.s. units respectively.

Water flows at the rate of  $0.1500kg/min$ through a tube and is heated by a heater dissipating $25.2W.$ The inflow and outflow water temperature are$15.2°C and 17.4°C$ respectively. When the rate of flow is increased to $0.2318kg/min$ and the rate of heating to $37.8W,$ the inflow and outflow temperature are unaltered. Find
i) the specific heat capacity of water
ii) the rate of loss of heat from the tube.

A uniform rod of length L, thermal conductivity K is connected from one end to a furnace at temperature $T_1$. The other end of rod is at temperature $T_2$​ and is exposed to atmosphere. The temperature of atmospheric is Ts​. The lateral part of rod is insulated. If $T2-Ts<<Ts, T2=Ts+\Delta T \& \Delta T\propto \left(T1-Ts\right)$, find proportionality constant of given equation. The heat loss to atmosphere is through radiation only and the emissivity of the rod is $\epsilon$.