There is formation of layer of snow $x\,cm$ thick on water, when the temperature of air is $ - {\theta ^o}C$ (less than freezing point). The thickness of layer increases from $x$ to $y$ in the time $t$, then the value of $t$is given by
$\frac{{(x + y)(x - y)\rho L}}{{2k\theta }}$
$\frac{{(x - y)\rho L}}{{2k\theta }}$
$\frac{{(x + y)(x - y)\rho L}}{{k\theta }}$
$\frac{{(x - y)\rho Lk}}{{2\theta }}$
An ice cube of dimensions $60\,cm \times 50\,cm \times 20\,cm$ is placed in an insulation box of wall thickness $1\,cm$. The box keeping the ice cube at $0^{\circ}\,C$ of temperature is brought to a room of temperature $40^{\circ}\,C$. The rate of melting of ice is approximately. (Latent heat of fusion of ice is $3.4 \times 10^{5}\,J\,kg ^{-1}$ and thermal conducting of insulation wall is $0.05\,Wm ^{-10} C ^{-1}$ )
Two rectangular blocks, having indentical dimensions, can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure, On of the blocks has thermal conductivity $k$ and the other $2 \ k$. The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9\ s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is :
Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12\,minutes$ when they are jointed in series. If now both the rods are joined in parallel, then the same amount of heat $\Delta Q$ will flow in ........ $\min$
A copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$, respectively. The thermal conductivity of copper is $0.38 kW / m /{ }^{\circ} C$. In the steady state, the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$
A heat source at $T = 10^3\, K$ is connected to another heat reservoir at $T = 10^2\, K$ by a copper slab which is $1\, m$ thick. Given that the thermal conductivity of copper is $0.1\, WK^{-1}\, m^{-1}$, the energy flux through it in the steady state is ........... $Wm^{-2}$