$1\, g$ of a steam at $100°C$ melt ........ $gm$ ice at $0°C\,?$ $($Latent heat of ice $= 80 \,cal/gm$ and latent heat of steam $= 540\, cal/gm)$

Morning breakfast gives $5000 \,cal$ to a $60 \,kg$ person. The efficiency of person is $30 \%$. The height upto which the person can climb up by using energy obtained from breakfast is ......... $m$

Ice at $0^o C$ is added to $200 \,\,g$ of water initially at $70^o C$ in a vacuum flask. When $50\,\, g$ of ice has been added and has all melted the temperature of the flask and contents is $40^o C$. When a further $80\,\,g$ of ice has been added and has all metled, the temperature of the whole is $10^o C$. Calculate the specific latent heat of fusion of ice.[Take $S_w =1\,\, cal /gm ^o C$.]

Pure water super cooled to $-15^o C$ is contained in a thermally insulated flask. Small amount of ice is thrown into the flask. The fraction of water frozen into ice is :

$10\, gm$ of ice at $0°C$ is mixed with $100 \,gm $ of water at $50°C.$ What is the resultant temperature of mixture........ $^oC$

A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ grams is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \ \mathrm{gm}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is