$37 \ g$ of ice at $0^{\circ} C$ temperature is mixed with $74 \ g$ of water at $70^{\circ} C$ temperature. The resultant temperature is (Specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of ice $= 80 \ cal \ g^{-1}$) (in $^{\circ} C$)

The temperature of water of mass $100 \ g$ is raised from $24^{\circ} C$ to $90^{\circ} C$ by adding steam to it. The mass of the steam added is (Latent heat of steam $= 540 \ cal \ g^{-1}$ and specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$) (in $g$)

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 liquids $A$ and $B$ are at $32^{\circ}C$ and $24^{\circ}C$. When mixed in equal masses,the temperature of the mixture is found to be $28^{\circ}C$. Their specific heats are in the ratio of:

$A$ coffee maker makes coffee by passing steam through a mixture of coffee powder,milk,and water. If the steam is mixed at the rate of $50 \, g/min$ in a mug containing $500 \, g$ of mixture,then it takes about $t_0$ seconds to make coffee at $70^{\circ} C$ when the initial temperature of the mixture is $25^{\circ} C$. The value of $t_0$ is close to .......... $s$ (ratio of latent heat of evaporation to specific heat of water is $540^{\circ} C$ and specific heat of the mixture can be taken to be the same as that of water).

$A$ calorimeter has a heat capacity of $100 \ J/K$ and is at $30^{\circ}C$. $100 \ g$ of water at $40^{\circ}C$ (specific heat capacity $4200 \ J/kg \cdot K$) is poured into the calorimeter. What is the final temperature of the mixture in the calorimeter in $^{\circ}C$?