$2 \mathrm{kg}$ of ice at $-20 °\mathrm{C}$ is mixed with $5 \mathrm{kg}$ of water at $20 °\mathrm{C}$ in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container. It is given that the specific heats of water and ice are $1 \mathrm{kcal} {\mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$ and $0.6 \mathrm{kcal} {\mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$, while the latent heat of fusion of ice $\left(L_{\mathrm{i}}\right)$ is $80 \mathrm{kcal} {\mathrm{kg}}^{-1}$.

In an industrial process $10 \mathrm{kg}$ of water per hour is to be heated from $20 °\mathrm{C}$ to $80°\mathrm{C}$. To do this, steam at $150 °\mathrm{C}$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90 °\mathrm{C}$, how many $\mathrm{kg}$ of steam is required per hour.

(Specific heat of steam, $c_{\mathrm{s}}=1 \mathrm{kcal} {\mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$, Latent heat of vaporisation, $L_{\mathrm{v}}=540 \mathrm{kcal} {\mathrm{kg}}^{-1}$and specific heat of water, $c_{\mathrm{w}}=1 \mathrm{kcal} {\mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$)

Which of the substances $A, B$ and $C$ has the lowest heat capacity, if heat is supplied to all of them at equal rates? The temperature versus time graph is shown below:

The portion $AB$ of the indicator diagram representing the state of matter denotes

Two substances $A$ and $B$ of equal mass $m$ are heated at a uniform rate of $6 \mathrm{cal} {\mathrm{s}}^{-1}$ under similar conditions. A graph between temperature and time is shown in the figure. The ratio of heat absorbed $\frac{H_{\mathrm{A}}}{H_{\mathrm{B}}}$ by them for complete fusion is