$19 \ g$ 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 $= 80 \ cal \ g^{-1}$.

$A$ sphere of $0.047 \; kg$ aluminium is placed for a sufficient time in a vessel containing boiling water,so that the sphere is at $100 \; ^{\circ}C$. It is then immediately transferred to a $0.14 \; kg$ copper calorimeter containing $0.25 \; kg$ water at $20 \; ^{\circ}C$. The temperature of the water rises and attains a steady state at $23 \; ^{\circ}C$. Calculate the specific heat capacity of aluminium in $kJ \; kg^{-1} K^{-1}$.

When $50 \ g$ of water at $10^{\circ} C$ is mixed with $50 \ g$ of water at $100^{\circ} C$,the resultant temperature is: (in $^{\circ} C$)

$M$ grams of steam at $100^{\circ} C$ is mixed with $200 \; g$ of ice at its melting point in a thermally insulated container. If it produces liquid water at $40^{\circ} C$ [heat of vaporization of water is $540 \; cal/g$ and heat of fusion of ice is $80 \; cal/g$],the value of $M$ is:

$A$ calorimeter contains $0.2\, kg$ of water at $30\,^{\circ}C$. $0.1\, kg$ of water at $60\,^{\circ}C$ is added to it. The mixture is well stirred and the resulting temperature is found to be $35\,^{\circ}C$. The thermal capacity of the calorimeter is .......... $J/K$.

In an experiment,a sphere of aluminium of mass $0.20\, kg$ is heated up to $150\, ^\circ C$. Immediately,it is put into water of volume $150\, cc$ at $27\, ^\circ C$ kept in a calorimeter of water equivalent $0.025\, kg$. The final temperature of the system is $40\, ^\circ C$. The specific heat of aluminium is ............ $J/kg\cdot ^\circ C$ (take $4.2\, J = 1\, cal$).