A liquid at 30$$^\circ $$C is poured very slowly into a Calorimeter that is at temperature of 110$$^\circ $$C. The boiling temperature of the liquid is 80$$^\circ $$C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50$$^\circ $$C. The ratio of the latent heat of the liquid to its specific heat will be ...........$$^\circ $$C.

[Neglect the heat exchange with surrounding]

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $${T_1} = 300\,K$$ and $${T_2} = 100\,K$$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller once and the thermal conductivities of the materials of the smaller and the larger cylinders are $${K_1}$$ and $${K_2}$$ respectively. If the temperature at the junction of the two cylinders in the steady state is $$200$$ $$K,$$ then $${K_1}/{K_2} = $$ ______________.

A drop of liquid of radius $$R = {10^{ - 2}}\,m$$ having surface tension $$S = {{0.1} \over {4\pi }}N{m^{ - 1}}$$ divides itself into $$K$$ identical drops. In this process the total change in the surface energy $$\Delta U = {10^{ - 3}}\,J.$$ If $$K = {10^\alpha }$$ then the value of $$\alpha $$ is

Consider two solid spheres P and Q each of density 8 gm cm^–3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm^–3 and viscosity $$\eta $$ = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm^–3 and viscosity $$\eta $$ = 2 poiseulles. The ratio of the terminal velocities of P and Q is