Six identical conducting rods are joined as shown. The ends $A$ and $D$ are maintained at $200\,^oC$ and $20\,^oC$ respectively. No heat is lost to surroundings. The temperature of the junction $C$ will be ........ $^oC$

A cylindrical rod with one end in a steam chamber and the outer 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 material of second rod is $1/4$ that of first, the rate at which ice melts is $gm/sec$ will be

The amount of heat required to change $1\ gm (0^o C)$ of ice into water of $100^o C$, is ............ $\mathrm{cal}$

Three liquids with masses $m_1,m_2,m_3$ are thoroughly mixed. If their specific heats are $c_1,c_2,c_3$ and their temperatures $T_1,T_2,T_3$ respectively, then the temperature of the mixture is

If the earth suddenly stops revolving and all its rotational $KE$ is used up in raising its temperature and if $'s'$ is taken to be the specific heat of the earth's material, the rise of temperature of the earth will be : ( $R -$ radius of the earth and $\omega  =$ its angular velocity, $J =\,Joule$ constant)

The coefficient of apparent expansion of mercury in a glass vessel is  $153 × 10^{-6}{°C^{-1}}$ and in a steel vessel is $144 × 10^{-6}{°C^{-1}}$. If $\alpha$ for steel is $12 × 10^{-6}{°C^{-1}}$, then that of glass is