The time taken for a calorimeter containing $75 \ g$ of water at $62^{\circ} C$ to cool to $58^{\circ} C$ is $9 \ minutes$. When the calorimeter contains $105 \ g$ of water,it takes $12 \ minutes$ to cool from $62^{\circ} C$ to $58^{\circ} C$. The water equivalent of the calorimeter is $.........$ (in $g$)

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.

$5 \ g$ of ice at $-30^{\circ} C$ and $20 \ g$ of water at $35^{\circ} C$ are mixed together in a calorimeter. The final temperature of the mixture is (Neglect heat capacity of the calorimeter,specific heat capacity of ice $= 0.5 \ cal \ g^{-1} {}^{\circ} C^{-1}$,latent heat of fusion of ice $= 80 \ cal \ g^{-1}$,and specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$). (in $^{\circ} C$)

$4 \text{ g}$ of steam at $100^{\circ} C$ is added to $20 \text{ g}$ of water at $46^{\circ} C$ in a container of negligible mass. Assuming no heat is lost to the surroundings, the mass of water in the container at thermal equilibrium is. (Latent heat of vaporisation $= 540 \text{ cal/g}$, Specific heat of water $= 1 \text{ cal/g}^{\circ} C$):- (in $\text{ g}$)

$A$ $10 \,kW$ drilling machine is used to drill a bore in an aluminium block of mass $25 \,kg$. If the machine is on for $3 \,minutes$ and $50 \%$ of the heat liberated is absorbed by the block, what is the rise in temperature of the block (in $^{\circ} C$)? (Specific heat of aluminium is $900 \,J \,kg^{-1} \,K^{-1}$)

Three containers $C_{1}, C_{2}$ and $C_{3}$ have water at different temperatures. The table below shows the final temperature $T$ when different amounts of water (given in litres) are taken from each container and mixed (assume no loss of heat during the process).

$C_{1}$	$C_{2}$	$C_{3}$	$T$
$1 \ l$	$2 \ l$	$-$	$60^{\circ} C$
$-$	$1 \ l$	$2 \ l$	$30^{\circ} C$
$2 \ l$	$-$	$1 \ l$	$60^{\circ} C$
$1 \ l$	$1 \ l$	$1 \ l$	$\theta$

The value of $\theta$ (in $^{\circ} C$ to the nearest integer) is