$250\,g$ of water and an equal volume of alcohol of mass $200\,g$ are placed successively in the same calorimeter and cool from $60^{\circ}C$ to $55^{\circ}C$ in $130\,s$ and $67\,s$ respectively. If the water equivalent of the calorimeter is $10\,g$,then the specific heat of alcohol in $\text{cal/g}^{\circ}C$ is:

The pressure and volume of saturated water vapour are $P$ and $V$ respectively. It is compressed isothermally such that the volume becomes $V/2$. The final pressure will be

If liquefied oxygen at $1$ atmospheric pressure is heated from $50\, K$ to $300\, K$ by supplying heat at a constant rate,the graph of temperature vs. time will be:

$A$ block of ice at $0^{\circ}C$ falls from a height of $1 \ km$ onto an insulating surface. If all its kinetic energy is converted into heat,what fraction of the ice will melt? (Take $g = 10 \ m/s^{2}$ and latent heat of fusion of ice $L = 3.36 \times 10^{5} \ J/kg$)

$A$ 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 $1000 \text{ kg m}^{-3}$)

$500\, g$ of water and $100\, g$ of ice at $0\,^{\circ}C$ are in a calorimeter whose water equivalent is $40\, g$. $10\, g$ of steam at $100\,^{\circ}C$ is added to it. Then the final amount of water in the calorimeter is ....... $g$ (Latent heat of ice $= 80\, cal/g$,Latent heat of steam $= 540\, cal/g$).