The temperature of the water of a pond is 0$$^\circ$$C while that of the surrounding atmosphere is $$-$$20$$^\circ$$C. If the density of ice is $$\rho$$, coefficient of thermal conductivity is k and latent heat of melting is L, then the thickness Z of ice layer formed increases as a function of time t is

The temperature of a blackbody radiation enclosed in a container of volume V is increased from 100$$^\circ$$C to 1000$$^\circ$$C. The heat required in the process is