$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature $T$. If these two liquids are mixed, the resulting temperature of the mixture is:

$540 \ g$ of ice at $0 \ ^\circ C$ is mixed with $540 \ g$ of water at $80 \ ^\circ C$. The final temperature of the mixture is

The temperatures of two liquids $A$ and $B$ are $32 \, ^\circ C$ and $24 \, ^\circ C$ respectively. When equal masses of both are mixed,the temperature of the mixture becomes $28 \, ^\circ C$. The ratio of their specific heats is .....

An aluminium piece of mass $50 \,g$ initially at $300^{\circ} C$ is dipped quickly and taken out of $1 \,kg$ of water,initially at $30^{\circ} C$. If the temperature of the aluminium piece immediately after being taken out of the water is found to be $160^{\circ} C$,the temperature of the water is ............ $^{\circ} C$. The specific heat capacities of aluminium and water are $900 \,J \,kg^{-1} K^{-1}$ and $4200 \,J \,kg^{-1} K^{-1}$,respectively.

$1\,\,kg$ of ice at $-10^{\circ}C$ is mixed with $4.4\,\,kg$ of water at $30^{\circ}C$. The final temperature of the mixture is $........^{\circ}C$ (specific heat of ice is $2100\,\,J/kg/K$ and latent heat of fusion of ice is $336000\,\,J/kg$)

$A$ small quantity,mass $m$,of water at a temperature $\theta$ (in $^oC$) is poured onto a large mass $M$ of ice which is at its melting point. If $c$ is the specific heat of water and $L$ is the latent heat of fusion of ice,then the mass of ice melted is given by