$A$ mass $m$ of material exists in its solid state at its melting temperature $0^\circ C$. The following processes occur to the material:
Process-$1$: An amount of thermal energy $Q$ is added to the material, and $\frac{2}{3}$ of the material melts.
Process-$2$: An identical additional amount of thermal energy $Q$ is added to the material, and the material is now a liquid at $40^\circ C$.
What is the ratio of the latent heat of fusion $(L)$ to the specific heat of the liquid $(s)$ for this material?

Heat energy of $184\,kJ$ is given to ice of mass $600\,g$ at $-12^{\circ}\,C$. The specific heat of ice is $2222.3\,J\,kg^{-1\circ}C^{-1}$ and the latent heat of fusion of ice is $336\,kJ\,kg^{-1}$.
$(A)$ Final temperature of the 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 freezing point of a liquid decreases when pressure is increased,if the liquid:

The figure shows a glass tube (linear coefficient of expansion is $\alpha$) completely filled with a liquid of volume expansion coefficient $\gamma$. On heating,the length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$.

The heat extracted out of $x \ \text{g}$ of water initially at $50^\circ \text{C}$ to cool it down to $0^\circ \text{C}$ is sufficient to evaporate $(1000 - x) \ \text{g}$ of water also initially at $50^\circ \text{C}$. The value of $x$ (closest integer) is . . . . . . . (Take latent heat of water $L = 2256 \ \text{kJ/kg}$, specific heat capacity of water $c = 4200 \ \text{J/kg}\cdot \text{K}$)

Find the quantity of heat required to convert $40 \; g$ of ice at $-20^{\circ} C$ into water at $20^{\circ} C$. Given $L_{\text{ice}} = 0.336 \times 10^6 \; J/kg$,specific heat of ice $= 2100 \; J/kg \cdot K$,and specific heat of water $= 4200 \; J/kg \cdot K$. (in $; J$)