$A$ $100 \, g$ of iron nail is hit by a $1.5 \, kg$ hammer striking at a velocity of $60 \, ms^{-1}$. What will be the rise in the temperature of the nail in $^{\circ}C$ if one-fourth of the energy of the hammer goes into heating the nail? [Specific heat capacity of iron $= 0.42 \, Jg^{-1} {}^{\circ}C^{-1}$]

$A$ glass flask of volume $1$ litre is fully filled with mercury at $0\,^{\circ}C$. Both the flask and mercury are now heated to $100\,^{\circ}C$. If the coefficient of volume expansion of mercury is $1.82 \times 10^{-4}/^{\circ}C$ and the coefficient of linear expansion of glass is $10 \times 10^{-6}/^{\circ}C$,the amount of mercury which is spilled out is ............ $ml$. (in $.2$)

One $kg$ of water, at $20, ^oC$, is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20, \Omega$. The rms voltage in the mains is $200, V$. Ignoring heat loss from the kettle, the time taken for water to evaporate fully is close to.......... $min$. [Specific heat of water $= 4200, J/kg, ^oC$, Latent heat of water $= 2260, kJ/kg$]

The variation of density of water with temperature is represented by the

$A$ gun fires a lead bullet of temperature $300 \ K$ into a wooden block. The bullet having a melting temperature of $600 \ K$ penetrates into the block and melts down. If the total heat required for the process is $625 \ J$,then the mass of the bullet is . . . . . . grams. (Latent heat of fusion of lead $= 2.5 \times 10^4 \ J \ kg^{-1}$ and specific heat capacity of lead $= 125 \ J \ kg^{-1} K^{-1}$)

Calculate the amount of heat (in calories) required to convert $5\,g$ of ice at $0^{\circ}C$ to steam at $100^{\circ}C$.