Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $30$ minutes. The ratio of their thermal conductivities will be

A copper rod and a steel rod of equal cross-sections and lengths $(L)$ are joined side by side and connected between two heat baths as shown in the figure

If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and conductivities of the metals are $K_{cu}$ and $K_{steel}$ $(K_{cu} > K_{steel}),$ then the temperature varies as (convection and radiation are negligible)

A copper rod $2\,m$ long has a circular cross-section of radius $1\, cm$. One end is kept  at $100^o\,C$ and the other at $0^o\,C$ and the surface is covered by nonconducting material to check the heat losses through the surface. The thermal  resistance of the bar in degree kelvin per watt is (Take thermal conductivity $K = 401\, W/m-K$ of copper):-

A body of length 1m having cross sectional area $0.75\;m^2$ has heat flow through it at the rate of $ 6000\; Joule/sec$ . Then find the temperature difference if $K = 200\;J{m^{ - 1}}{K^{ - 1}}$ ...... $^oC$

The coefficient of thermal conductivity depends upon

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to