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

$50 \,g$ ice at $0^{\circ} C$ is dropped into a calorimeter containing $100 \,g$ water at $30^{\circ} C$. If thermal capacity of calorimeter is zero then amount of ice left in the mixture at equilibrium is .......... $g$

In a calorimeter of water equivalent $20 \,g$, water of mass $1.1 \,kg$ is taken at $288 \,K$ temperature. If steam at temperature $373 \,K$ is passed through it and temperature of water increases by $6.5^{\circ} C$ then the mass of steam condensed is ............ $g$

Two identical blocks of metal are at $20^{\circ} C$ and $80^{\circ} C$, respectively. The specific heat of the material of the two blocks increases with temperature. Which of the following is true about the final temperature $T_f$ when the two blocks are brought into contact (assuming that no heat is lost to the surroundings)?

A block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to a $3\, kg$ water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container

A $100 \,g$ of iron nail is hit by a $1.5\, kg$ hammer striking at a velocity of $60\, ms ^{-1}$. $............^{\circ}C$ will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail .

[Specific heat capacity of iron  $=0.42\, Jg ^{-1}{ }\,^{\circ}C ^{-1}$ ]