When $M_1$ gram of ice at $-10\,^{\circ}C$ (specific heat $= 0.5\, cal\, g^{-1}\,^{\circ}C^{-1}$) is added to $M_2$ gram of water at $50\,^{\circ}C$,finally no ice is left and the water is at $0\,^{\circ}C$. The value of latent heat of ice,in $cal\, g^{-1}$ is

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 the temperature of the water increases by $6.5^{\circ} C$,then the mass of steam condensed is ............ $g$.

When $50 \ g$ of water at $10^{\circ} C$ is mixed with $50 \ g$ of water at $100^{\circ} C$,the resultant temperature is: (in $^{\circ} C$)

$A$ coffee maker makes coffee by passing steam through a mixture of coffee powder,milk,and water. If the steam is mixed at the rate of $50 \, g/min$ in a mug containing $500 \, g$ of mixture,then it takes about $t_0$ seconds to make coffee at $70^{\circ} C$ when the initial temperature of the mixture is $25^{\circ} C$. The value of $t_0$ is close to .......... $s$ (ratio of latent heat of evaporation to specific heat of water is $540^{\circ} C$ and specific heat of the mixture can be taken to be the same as that of water).

One kilogram of ice at $0^{\circ}C$ is mixed with one kilogram of water at $80^{\circ}C$. The final temperature of the mixture is ........ $^{\circ}C$. (Take: specific heat of water $= 4200 \ J \ kg^{-1} \ K^{-1}$,latent heat of ice $= 336 \ kJ \ kg^{-1}$)

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