Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$, respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $\theta_2$ and $\theta_1$ respectively $\left( {\theta _2} > {\theta _1} \right)$ . The temperature at the interface is
$\frac{\theta_2 + \theta_1}{2}$
$\frac{\theta _1}{10} + \frac{9\theta _2}{10}$
$\frac{\theta_1}{3} + \frac{2\theta_2}{3}$
$\frac{\theta _1}{6} + \frac{5\theta _2}{6}$
A metallic rod of cross-sectional area $9.0\,\,cm^2$ and length $0.54 \,\,m$, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \,\,gm$ for every $33 \,\,sec$. The thermal conductivity of the rod is ....... $ Wm^{-1} K^{-1}$
Ice starts forming in lake with water at ${0^o}C$ and when the atmospheric temperature is $ - {10^o}C$. If the time taken for $1 \;cm$ of ice be $7$ hours, then the time taken for the thickness of ice to change from $1\; cm$ to $2\; cm$ is
Four rods of silver, copper, brass and wood are of same shape. They are heated together after wrapping a paper on it, the paper will burn first on
Three rods made of the same material and having the same cross section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at ${0^o}C$ and ${90^o}C$ respectively. The temperature of the junction of the three rods will be ...... $^oC$
The two ends of a metal rod are maintained at temperatures $100 ^o C$ and $110^o C$. The rate of heat flow in the rod is found to be $4.0\ J/s$. If the ends are maintained at temperatures $200^o\ C$ and $210^o\ C$, the rate of heat flow will be.... $J/s$