$300\, gm$ of water at $25°C$ is added to $100\, gm$ of ice at $0°C$. The final temperature of the mixture is…….. $^oC$

A $2\,kg$ copper block is heated to $500^o\,C$ and then it is placed on a large block of ice  at $0^o\,C$. If the specific heat capacity of copper is $400\, J/kg/ ^o\,C$ and latent heat of  fusion of water is $3.5 \times 10^5\, J/kg$, the amount of ice, that can melt is :-

Heat is being supplied at a constant rate to a sphere of ice which is melting at the rate of $0.1 \,\,gm/sec$. It melts completely in $100\,\,sec$. The rate of rise of temperature thereafter will be ……..$^oC/\sec$ (Assume no loss of heat.)

A calorimeter of water equivalent $20\, g$ contains $180\, g$ of water at $25^{\circ} C$. '$m$' grams of steam at $100^{\circ} C$ is mixed in it till the temperature of the mixure is $31^{\circ} C$. The value of $'m'$ is close to

(Latent heat of water $=540$ cal $g ^{-1}$, specific heat of water $=1$ cal $g^{-1}{ }^{\circ} C ^{-1}$ )

$100\,g$ of water is supercooled to $-\,10\,^oC$. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze ? $[S_W = 1\,cal\,g^{-1}\,^oC^{-1}$ and ${L^W}_{{\text{fussion}}}$ $= 80\,cal\,g^{-1}]$