$10 \, g$ of ice at $0^{\circ}C$ is mixed with $100 \, g$ of water at $50^{\circ}C$. What is the resultant temperature of the mixture in $^{\circ}C$?

$150 \,g$ of ice is mixed with $100 \,g$ of water at temperature $80^{\circ} C$. The latent heat of ice is $80 \,cal/g$ and the specific heat of water is $1 \,cal/g^{\circ} C$. Assuming no heat loss to the environment,the amount of ice which does not melt is ........... $g$.

$A$ copper ball of mass $100 \ gm$ is at a temperature $T$. It is dropped into a copper calorimeter of mass $100 \ gm$,filled with $170 \ gm$ of water at room temperature. Subsequently,the temperature of the system is found to be $75 ^\circ C$. $T$ is given by......$^\circ C$ (Given: room temperature $= 30 ^\circ C$,specific heat of copper $= 0.1 \ cal/gm ^\circ C$)

$10 \, g$ of ice at $0 \, ^oC$ is mixed with $m \, g$ of water at $50 \, ^oC$. What is the minimum value of $m$ (in $g$) so that the ice melts completely? (Given: $L_f = 80 \, cal/g$ and $S_W = 1 \, cal/g \cdot ^oC$)

$10 \ kg$ of ice at $-10^{\circ}C$ is added to $100 \ kg$ of water to lower its temperature from $25^{\circ}C.$ Consider no heat exchange to surroundings. The decrement to the temperature of water is . . . . . . $^{\circ}C.$ (specific heat of ice $= 2100 \ J/kg.^{\circ}C$, specific heat of water $= 4200 \ J/kg.^{\circ}C$, latent heat of fusion of ice $= 3.36 \times 10^{5} \ J/kg$)

Two liquids $A$ and $B$ are at temperatures of $75^{\circ} C$ and $15^{\circ} C$. Their masses are in the ratio of $2: 3$ and their specific heats in the ratio $3: 4$. If these two liquids are mixed,then the resulting temperature will be $...^{\circ} C$.