$80 \ gm$ of water at $30 \ ^\circ C$ is poured onto a large block of ice at $0 \ ^\circ C$. The mass of ice that melts is .... $gm$

$A$ metal block of mass $3.3 \ kg$ is heated to a temperature of $400^{\circ} C$ and then placed on a large ice block. The specific heat of the metal is $0.4 \ J \ g^{-1} \ K^{-1}$ and the latent heat of fusion of water is $330 \ J \ g^{-1}$. The maximum amount of ice that can melt is: (in $kg$)

Steam at $100\,^{\circ}C$ is passed into $20\,g$ of water at $10\,^{\circ}C$. When water acquires a temperature of $80\,^{\circ}C$,the mass of water present will be ........ $g$. [Take specific heat of water $= 1\,cal\,g^{-1}\,^{\circ}C^{-1}$ and latent heat of steam $= 540\,cal\,g^{-1}$]

$A$ liquid of mass $2m$ and specific heat $C$ is heated to a temperature $4T$. Another liquid of mass $m$ and specific heat $2C$ is heated to a temperature $T$. If these two liquids are mixed,the resulting temperature of the mixture is:

$10 \, g$ of ice at $-20^{\circ} C$ is kept in a calorimeter containing $10 \, g$ of water at $10^{\circ} C$. The specific heat of water is twice that of ice. When equilibrium is reached, the calorimeter will contain ..........

When $M_1$ gram of ice at $-10\,^{\circ}C$ (specific heat $= 0.5\, cal\, g^{-1}\,^{\circ}C^{-1}$) is added to $M_2$ gram of water at $50\,^{\circ}C$,finally no ice is left and the water is at $0\,^{\circ}C$. The value of latent heat of ice,in $cal\, g^{-1}$ is