Steam at $100^{\circ}C$ is passed into a calorimeter containing $1\,kg$ of water with a water equivalent of $0.02\,kg$ at $15^{\circ}C$ until the temperature of the calorimeter rises to $80^{\circ}C$. The mass of the steam condensed is $.....\,kg$. (Given: $L = 536\,cal/g$,specific heat of water $c = 1\,cal/g^{\circ}C$)

When $0.4 \ kg$ of water at $30^{\circ} C$ is mixed with $0.15 \ kg$ of water at $25^{\circ} C$ in a calorimeter,the final temperature is found to be $27^{\circ} C$. Find the water equivalent of the calorimeter. (in $kg$)

$10 \, g$ 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 $S_W = 1 \, cal/g \cdot ^oC$)

Steam at $100^{\circ} C$ is passed into $1 \ kg$ of water contained in a calorimeter of water equivalent $0.2 \ kg$ at $9^{\circ} C$ until the temperature of the calorimeter and water in it increases to $90^{\circ} C$. The mass of steam condensed in $kg$ is nearly (specific heat of water $= 1 \ cal/g^{\circ} C$, latent heat of vaporisation $= 540 \ cal/g$)

$A$ water heater of power $2000\,W$ is used to heat water. The specific heat capacity of water is $4200\,J\,kg^{-1}\,K^{-1}$. The efficiency of the heater is $70\%$. The time required to heat $2\,kg$ of water from $10^{\circ}C$ to $60^{\circ}C$ is $..........s$. (Assume that the specific heat capacity of water remains constant over the temperature range).

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 .....