$19 \ g$ of water at $30^{\circ} C$ and $5 \ g$ of ice at $-20^{\circ} C$ are mixed together in a calorimeter. What is the final temperature of the mixture (in $^{\circ} C$)? Given specific heat of ice $= 0.5 \ cal \ g^{-1} (^{\circ} C)^{-1}$ and latent heat of fusion of ice $= 80 \ cal \ g^{-1}$.

The temperature of a copper piece of mass $50 \ g$ is raised by $10 \ ^\circ C$. If the same amount of heat is given to $10 \ g$ of water,the rise in its temperature is = ...... $^\circ C$ (Specific heat of copper $= 420 \ J/kg \cdot ^\circ C$,Specific heat of water $= 4200 \ J/kg \cdot ^\circ C$).

When $x \text{ grams}$ of steam at $100^{\circ}C$ is mixed with $y \text{ grams}$ of ice at $0^{\circ}C$,we obtain $(x + y) \text{ grams}$ of water at $100^{\circ}C$. What is the ratio $y/x$?

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$,while the other one is kept at $0^{\circ} C$. If the two are brought into contact,then assuming no heat loss to the environment,the final temperature that they will reach is

$A$ copper block of mass $5.0 \, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (in $kg$) that can melt? [Specific heat of copper: $0.39 \, J g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of water: $335 \, J g^{-1}$]

$A$ small quantity of water of mass $m$ at temperature $\theta^{\circ} C$ is mixed with a large mass $M$ of ice which is at its melting point. If $s$ is the specific heat capacity of water and $L$ is the latent heat of fusion of ice,then the mass of ice melted is: