The amount of heat required to change $1 \, g$ of ice at $0^\circ C$ into water at $100^\circ C$ is ............ $cal$.

$A$ 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?

$A$ waterfall is $84 \ m$ high. If half of the potential energy of the falling water gets converted to heat,the rise in temperature of the water will be: (in $^\circ C$)

The variation of density of water with temperature is represented by the

Water falls from a height of $210 \, m$. Assuming the whole of the energy due to the fall is converted into heat,the rise in temperature of water would be .......... $^\circ C$ $(J = 4.3 \, J/cal)$.

Two objects made of the same material have masses $m$ and $2m$ and are at temperatures $2T$ and $T$ respectively. When heat $Q$ is supplied to the object of mass $2m$,its temperature rises to $2T$. If the same heat $Q$ is supplied to the object of mass $m$,its temperature rises to: