$A$ metal ball of mass $100 \ g$ at $20^{\circ} C$ is dropped in $200 \ ml$ of water at $80^{\circ} C$. If the resultant temperature is $70^{\circ} C$,then the ratio of specific heat of the metal to that of water is

$A$ 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 $= 3.5 \times 10^{5}\,J\,kg^{-1}$]

How many grams of ice at $0 \, ^\circ \text{C}$ will be melted by $1 \, \text{g}$ of steam at $100 \, ^\circ \text{C}$? (Latent heat of fusion of ice $L = 80 \, \text{cal/g}$ and latent heat of vaporization of water $L' = 540 \, \text{cal/g}$)

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).

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 ........ $^\circ C$.

$A$ 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: