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 $S_w =1\,\, cal /gm ^o C$.]

A geyser heats water flowing at a rate of $2.0 kg$ per minute from $30^{\circ} C$ to $70^{\circ} C$. If geyser operates on a gas burner, the rate of combustion of fuel will be $\dots \; g \min ^{-1}$

[Heat of combustion $=8 \times 10^{3} Jg ^{-1}$  Specific heat of water $=4.2 Jg ^{-1} \; { }^{\circ} C ^{-1}$ ]

$20\, gm$ of boiling water is poured into an ice-cold brass vessel (specific heat $0.1\, cal/gm-\,^oC$) of mass $100\, gm$. The resulting temperature is ........ $^oC$

$0.1\,m^3$ of water at $80\,^oC$ is mixed with $0.3\,m^3$ of water at $60\,^oC$. The final temperature of the mixture is ........ $^oC$

The specific heat of water $=4200\, J\, kg ^{-1}\, K ^{-1}$ and the latent heat of ice $=3.4 \times 10^{5}\, J\, kg ^{-1}.$ $100$ grams of ice at $0^{\circ} C$ is placed in $200\, g$ of water at $25^{\circ} C$. The amount of ice that will melt as the temperature of water reaches $0^{\circ} C$ is close to (in $grams$) 

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box contains one mole of helium at temperature $(7/3)$ $T_0$ The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases,$T_f$  in terms of $T_0$ is