If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously, will be

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$  along the length $x$ of the bar from its hot end is best described by which of the following figures ?

A glass flask of volume $1$ litre is fully filled with mercury at $0\,^oC$. Both the flask and mercury are now heated to $100\,^oC$. If the coefficient of volume expansion of mercury is $1.82\times10^{-4}/^oC$, volume coefficient of linear expansion of glass is $10\times10^{-6}/^oC$, the amount of mercury which is spilted out is ………… $\mathrm{ml}$

Three rods of same dimensions have thermal conductivities $3K,\,2K$ and $K$. They are arranged as shown with their ends at $100\,^oC$, $50\,^oC$ and $0\,^oC$. Temperature of junction is

Two rods of same length and same area of cross section are joined

Temperature of two ends are as shown in figure. As we move along the rod, temperature are as shown in following