Value of temperature gradient is $80\,^oC/m$ on a rod of $0.5\,m$ length. Temperature of hot end is $30\,^oC$, then what is the temperature of cold end ?

Give definition, unit and dimensional formula of thermal conductivity.

Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$

The rate of heat flow through the cross-section of the rod shown in figure is ($T_2 > T_1$ and thermal conductivity of the material of the rod is $K$)

Assertion : The equivalent thermal conductivity of two plates of same thickness in contact is less than the smaller value of thermal conductivity.
Reason : For two plates of equal thickness in contact the equivalent thermal conductivity is given by : $\frac{1}{K} = \frac{1}{{{K_1}}} + \frac{1}{{{K_2}}}$

Two sheets of thickness $d$ and $3d$, are touching each other. The temperature just outside the thinner sheet side is $A$, and on the side of the thicker sheet is $C$. The interface temperature is $B. A, B$ and $C$ are in arithmetic progressing, the ratio of thermal conductivity of thinner sheet and thicker sheet is