If mass energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

$1\ gm$ of ice at $0^o C$ is mixed with $1gm$ of water at $100^o C$ the resulting temperature will be .......... $^oC$ 

Calorie is defined as the amount of heat required to raise temperature of $1g$ of water by $1°C$ and it is defined under which of the following conditions

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:

In an experiment a sphere of aluminium of mass $0.20\, kg$ is heated upto $150\,^oC$. Immediately, it is put into water of volume $150\, cc$ at $27\,^oC$ kept in a calorimeter of water equivalent to $0.025\, kg$. Final temperature of the system is $40\,^oC$. The specific heat of aluminium is ............ $J/kg\,-\,^oC$ (take $4.2\, Joule= 1\, calorie$)

A vessel contains $110\, g$ of water. The heat capacity of the vessel is equal to $10\, g$ of water. The initial temperature of water in vessel is $10°C.$ If $220\, g$ of hot water at $70°C$ is poured in the vessel, the final temperature neglecting radiation loss, will be........ $^oC$