$0.1 \,m^{3}$ of water at $80^{\circ} C$ is mixed with $0.3 \,m^{3}$ of water at $60^{\circ} C$. The final temperature of the mixture is (in $^{\circ} C$)

$2 \; g$ of steam condenses when passed through $40 \; g$ of water initially at $25 \; ^\circ C$. The condensation of steam raises the temperature of water to $54.3 \; ^\circ C$. What is the latent heat of steam in $cal/g$?

$A$ block of ice of mass $120\,g$ at temperature $0^{\circ}C$ is put in $300\,g$ of water at $25^{\circ}C$. The $x\,g$ of ice melts as the temperature of the water reaches $0^{\circ}C$. The value of $x$ is.
[Use: Specific heat capacity of water $= 4200\,J\,kg^{-1}K^{-1}$,Latent heat of ice $= 3.5 \times 10^{5}\,J\,kg^{-1}$]

$2 \ g$ of steam at $100 \ ^\circ C$ is passed into $40 \ g$ of water at $25 \ ^\circ C$. The final temperature of the mixture becomes $54.3 \ ^\circ C$. Find the latent heat of vaporization of steam in $cal/g$.

$A$ small quantity of water of mass $m$ at temperature $\theta^{\circ} C$ is mixed with a large mass $M$ of ice which is at its melting point. If $s$ is the specific heat capacity of water and $L$ is the latent heat of fusion of ice,then the mass of ice melted is:

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 $4.2\, J = 1\, cal$).