A liquid having coefficient of cubical expansion $\gamma $ is filled in the container having coefficient of linear expansion $\alpha $. If on heating the liquid overflows, then which of the following relations is correct?

$0^o C$ $1\ gm$ ice is mixed with $100^o C$ vapor then what wiil be the final temperature ($^o C$)? 

A substance of mass $m\,kg$ requires a power input of $P$ $watt$ to remain in the molten state at its melting point. When the power is turned off, the substance completely solidifies in time $t\,sec$. The latent heat of fusion of the substance 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 $= 420\,J-kg^{-1}\,^oC^{-1}$ )

The density of water at $20^oC$ is $0.998\, gm/cm^3$ and at $40^oC$ is $0.992\, gm/cm^3$. The mean coefficient of cubical expansion (in per $^oC$) is :-

A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temp is lowered until the Fahrenheit temp. register $140^o$. What is the fall in the temperature as registered by centigrade thermometer ....... $^oC$