Two bars of thermal conductivities $K$ and $3K$ and lengths $1\,\, cm$ and $2\,\, cm$ respectively have equal cross-sectional area, they are joined lengths wise as shown in the figure. If the temperature at the ends of this composite bar is $0\,^oC$ and $100\,^oC$ respectively (see figure), then the temperature $\varphi $ of the interface is......... $^oC$
$50$
$\frac{{100}}{3}$
$60$
$\frac{{200}}{3}$
The temperature gradient in a rod of $0.5 m$ long is ${80^o}C/m$. If the temperature of hotter end of the rod is ${30^o}C$, then the temperature of the cooler end is ...... $^oC$
One end of a copper rod of length $1.0\;m$ and area of cross-section ${10^{ - 3}}$ is immersed in boiling water and the other end in ice. If the coefficient of thermal conductivity of copper is $92\;cal/m{\rm{ - }}s{{\rm{ - }}^o}C$ and the latent heat of ice is $8 \times {10^4}cal/kg$, then the amount of ice which will melt in one minute is
On a cold morning, a metal surface will feel colder to touch than a wooden surface because
The ends of two rods of different materials with their thermal conductivities, radii of cross-sections and lengths all are in the ratio $1:2$ are maintained at the same temperature difference. If the rate of flow of heat in the larger rod is $4\;cal/\sec $, that in the shorter rod in $cal/\sec $ will be