One kilogram of ice at $0\,^oC$ is mixed with one kilogram of water at $80\,^oC$. Temperature of mixture is ........ $^oC$  (specific heat of water $= 4200\,J\,kg^{-1}\,K^{-1}$ and latent heat of ice $= 336\,KJ \,kg^{-1}$ )

Two rods, one made of aluminium and the other made of steel, having initial lengths $l_1$  and $l_2$ respectively are connected together to form a single rod of length $(l_1 + l_2)$. The coefficients of linear expansion for aluminium and steel of $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount when  their temperature is raised by $t^oC$, then the ratio $l_1/(l_1 + l_2)$ :-

Four rods of same material with different radii $r$ and length $l$ are used to connect two reservoirs of heat at different temperatures. Which one will conduct most heat ?

$200\, g$ of a solid ball at $20\,^oC$ is dropped in an equal amount of water at $80\,^oC$. The resulting temperature is $60\,^oC$. This means that specific heat of solid is

$50\,g$ of copper is heated to increase is temperature by $10\,^oC$. If the same quantity of heat is given to $10\,g$ of water, the rise in its temperature is  ........ $^oC$ (Specific heat of copper $= 420\,J-kg^{-1}\,^oC^{-1}$ )

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20^o\,C$, the coefficient of linear expansion (in per $^oC^{-1}$) of the metal is :-