We have half a bucket ($6$ litre) of water at $20^oC $.If we want water at $40^oC$, how much steam at $100^oC$ should be added to it ?

Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$, Specific heat of ice is $2222.3\,J\,kg ^{-1^{\circ}}\,C ^{-1}$ and latent heat of ice in $336\,kJ / kg ^{-1}$

$(A)$ Final temperature of system will be $0^{\circ} C$.

$(B)$ Final temperature of the system will be greater than $0^{\circ} C$.

$(C)$ The final system will have a mixture of ice and water in the ratio of $5: 1$.

$(D)$ The final system will have a mixture of ice and water in the ratio of $1: 5$.

$(E)$ The final system will have water only.

Choose the correct answer from the options given below:

Ice at $-20\,^oC$ is added to $50\,g$ of water at $40\,^oC.$ When the temperature of the mixture reaches $0\,^oC,$ it is found that $20\,g$ of ice is still unmelted. The amount of ice added to the water was close to ........$g$ (Specific heat of water $= 4.2\,J/g/^oC)$ Heat of fusion of water at $0^oC = 334\,J/g$ )

A refrigerator converts $500\,g$ of water at $25\,^oC$ into ice at $-10\,^oC$ in $3\,hours\,40\,minutes$ . The quantity of heat removed per minute is  ........ $cal/\min$

(Sp. heat of water $1\,cal/gm$, Specific heat of ice $= 0.5\,cal/g\,^oC$ , letent heat of fusion $= 80\,cal/g$ )

An aluminium piece of mass $50 \,g$ initially at $300^{\circ} C$ is dipped quickly and taken out of $1 \,kg$ of water, initially at $30^{\circ} C$. If the temperature of the aluminium piece immediately after being taken out of the water is found to be $160^{\circ} C$, the temperature of the water ............ $^{\circ} C$ Then, specific heat capacities of aluminium and water are $900 \,Jkg ^{-1} K ^{-1}$ and $4200 \,Jkg ^{-1} K ^{-1}$, respectively.

Latent heat of ice is $80 \,cal/gm$. A man melts $60\, g$ of ice by chewing in $1$ minute. His power is ........ $W$