$1 \,kg$ of ice at $-20^{\circ} C$ is mixed with $2 \,kg$ of water at $90^{\circ} C$. Assuming that there is no loss of energy to the environment,the final temperature of the mixture is ............ $^{\circ} C$. (Assume,latent heat of ice $= 334.4 \,kJ/kg$,specific heat of water and ice are $4.18 \,kJ \,kg^{-1} K^{-1}$ and $2.09 \,kJ \,kg^{-1} K^{-1}$,respectively.)

In an experiment on the specific heat of a metal,a $0.20 \; kg$ block of the metal at $150 \; ^{\circ}C$ is dropped in a copper calorimeter (of water equivalent $0.025 \; kg$) containing $150 \; cm^{3}$ of water at $27 \; ^{\circ}C$. The final temperature is $40 \; ^{\circ}C$. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible,is your answer greater or smaller than the actual value for the specific heat of the metal?

$A$ $210 \,W$ heater is used to heat $100 \,g$ of water. The time required to raise the temperature of this water from $25^{\circ} C$ to $100^{\circ} C$ is (specific heat capacity of water $= 4200 \,J / kg \cdot ^{\circ} C$). (in $\,s$)

$100 \, g$ of water is supercooled to $-10 \, ^\circ C$. At this point,due to some disturbance,some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze? $[S_W = 1 \, cal \, g^{-1} \, ^\circ C^{-1}$ and $L_{fusion} = 80 \, cal \, g^{-1}]$

In a waterfall,the water falls from a height of $100 \ m$. If the entire kinetic energy $(K.E.)$ of the water is converted into heat,the rise in temperature of the water will be ........ $^\circ C$.

Three copper blocks of masses $M_1, M_2$ and $M_3$ $kg$ respectively are brought into thermal contact until they reach equilibrium. Before contact,they were at temperatures $T_1, T_2, T_3$ $(T_1 > T_3)$. Assuming there is no heat loss to the surroundings,the equilibrium temperature $T$ is ($s$ is the specific heat of copper).