If the ratio of densities of two substances is $5:6$ and the ratio of their specific heat capacities is $3:5$,then the ratio of heat energies required per unit volume so that the two substances can have the same temperature rise is

The heat required to convert $1 \, g$ of ice at $0^{\circ}C$ into steam at $100^{\circ}C$ is (given $L_{f} = 80 \, cal/g$,$c_{w} = 1 \, cal/g^{\circ}C$,$L_{v} = 536 \, cal/g$):

Column $I$ gives some devices and Column $II$ gives some processes on which the functioning of these devices depends. Match the devices in Column $I$ with the processes in Column $II$.

Column $I$	Column $II$
$(A)$ Bimetallic strip	$(p)$ Radiation from a hot body
$(B)$ Steam engine	$(q)$ Energy conversion
$(C)$ Incandescent lamp	$(r)$ Melting
$(D)$ Electric fuse	$(s)$ Thermal expansion of solids

$A$ thermally insulated vessel contains $150\, g$ of water at $0\, ^oC$. Then the air from the vessel is pumped out adiabatically. $A$ fraction of water turns into ice and the rest evaporates at $0\, ^oC$ itself. The mass of evaporated water will be closest to ....... $g$ (Latent heat of vaporization of water $= 2.10 \times 10^6\, J/kg$ and Latent heat of fusion of water $= 3.36 \times 10^5\, J/kg$).

$A$ thermoelectric emf of $200 \, \mu V$ is generated between $0 \, ^oC$ and $100 \, ^oC$. The emf generated between $(0 \, ^oC - 32 \, ^oC)$ and $(32 \, ^oC - 70 \, ^oC)$ are $64 \, \mu V$ and $76 \, \mu V$ respectively. What is the thermo $emf$ generated between $(70 \, ^oC - 100 \, ^oC)$ in $\mu V$?

$A$ piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $h$ is (Latent heat of ice is $L = 3.4 \times 10^{5} \text{ J/kg}$ and $g = 10 \text{ N/kg}$) (in $\text{ km}$)