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:

The specific heat of a metal at low temperatures varies according to $S = aT^3$ where a is a constant and $T$ is the absolute temperature. The heat energy needed to raise unit mass of the metal from $T = 1 K$ to $T = 2 K$ is

Equal masses of three liquids $A, B$ and $C$ have temperatures $10\,^oC$, $25\,^oC$ and $40\,^oC$ respectively. If $A$ and $B$ are mixed, the mixture has a temperature of $15\,^oC$. If $B$ and $C$ are mixed then mixture has temperature of $30\,^oC$. If $A$ and $C$ are mixed, the mixture will have a temperature of ........ $^oC$

A copper ball of mass $100\ gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100\ gm$, filled with $170\  gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^o C$. $T$ is given by......$^oC$ (Given : room temperature $= 30^o  C$, specific heat of copper $=$ $0.1$ $cal/gm^o C$)

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

Work done in converting one gram of ice at $-10°C$ into steam at $100°C$ is ....... $J$