The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are $8 \Omega$ and $10 \Omega$ respectively. After inserting in a hot bath of temperature $400^{\circ} C$,the resistance of the platinum wire is: (in $\Omega$)

Two different liquids of same mass are kept in two identical vessels,which are placed in a freezer that extracts heat from them at the same rate,causing each liquid to transform into a solid. The schematic figure below shows the temperature $T$ versus time $t$ plot for the two materials. We denote the specific heat of materials in the liquid (solid) states to be $C_{L1}$ $(C_{S1})$ and $C_{L2}$ $(C_{S2})$,respectively. Choose the correct option given below.

Find the amount of heat supplied to decrease the volume of an ice-water mixture by $1 \, cm^3$ without any change in temperature. (Given: $\rho_{ice} = 0.9 \rho_{water}$,$L_{ice} = 80 \, cal/g$).

$A$ stationary object at $4^{\circ}C$ and weighing $3.5\, kg$ falls from a height of $2000\, m$ on a snow mountain at $0^{\circ}C$. If the temperature of the object just before hitting the snow is $0^{\circ}C$ and the object comes to rest immediately $(g = 10\, m/s^2)$ and (latent heat of ice $= 3.5 \times 10^5\, J/kg$),then the amount of ice that will melt is:

$A$ water cooler of storage capacity $120$ litres can cool water at a constant rate of $P$ watts. In a closed circulation system (as shown schematically in the figure),the water from the cooler is used to cool an external device that generates constantly $3 \text{ kW}$ of heat (thermal load). The temperature of water fed into the device cannot exceed $30^{\circ}\text{C}$ and the entire stored $120$ litres of water is initially cooled to $10^{\circ}\text{C}$. The entire system is thermally insulated. The minimum value of $P$ (in watts) for which the device can be operated for $3$ hours is (Specific heat of water is $4.2 \text{ kJ kg}^{-1} \text{K}^{-1}$ and the density of water is $1000 \text{ kg m}^{-3}$)

When $1\, g$ of water at $0^{\circ}C$ and $1 \times 10^5\, N/m^2$ pressure is converted into ice of volume $1.091\, cm^3$,the external work done will be (in $, J$)