The thermal conductivity of a rod is $2$. What is its thermal resistivity?

$A$ cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1 \ gm$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first,and if the thermal conductivity of the material of the second rod is $\frac{1}{4}$ that of the first,the rate at which ice melts in $gm/sec$ will be:

An aluminium rod of length $1 \,m$ and a steel rod of length $2 \,m$, both having the same cross-sectional area, are soldered together end-to-end. The thermal conductivity of the aluminium rod and the steel rod is $200 \,Js^{-1} \,m^{-1} \,K^{-1}$ and $50 \,Js^{-1} \,m^{-1} \,K^{-1}$ respectively. The temperatures of the free ends are maintained at $300 \,K$ and $500 \,K$. What is the temperature of the junction (in $\,K$)?

Three rods of the same dimensions have thermal conductivities $3K, 2K$, and $K$. They are arranged as shown in the figure. The temperature of the junction in the steady state is:

Two identical long bars $A$ and $B$ made of different materials are coated with wax and have one end immersed in a hot oil bath. When the steady state is reached, the lengths for which the wax melts are $l_A$ and $l_B$. If $k_A$ and $k_B$ are the thermal conductivities of the materials, then:

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 $\rho$, the coefficient of thermal conductivity is $k$, and the latent heat of melting is $L$, then the thickness $Z$ of the ice layer formed increases as a function of time $t$ as: