An aluminium container of mass $100 \, g$ contains $200 \, g$ of ice at $-20^{\circ} C$. Heat is added to the system at the rate of $100 \, cal/s$. The temperature of the system after $4$ minutes will be ....... $^{\circ} C$ (specific heat of ice $= 0.5 \, cal/g^{\circ} C$,latent heat of fusion $L = 80 \, cal/g$,specific heat of $Al = 0.2 \, cal/g^{\circ} C$,specific heat of water $= 1 \, cal/g^{\circ} C$)

Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

The surface of the lake is at $2^{\circ} C$. The temperature of the bottom of the lake is ....... $^{\circ} C$.

$A$ 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,then the quantity of ice that melts is (Acceleration due to gravity $= 10 \ m/s^2$,Latent heat of ice $= 3.5 \times 10^5 \ J/kg$)

The densities of wood and benzene at $0^{\circ} C$ are $880 \ kg \ m^{-3}$ and $900 \ kg \ m^{-3}$,respectively. The coefficients of volume expansion are $1.2 \times 10^{-3} \ ^{\circ}C^{-1}$ for wood and $1.5 \times 10^{-3} \ ^{\circ}C^{-1}$ for benzene. The temperature at which a piece of wood just sinks in benzene is (in $^{\circ} C$)

$Assertion :$ In the pressure-temperature $(P-T)$ phase diagram of water,the slope of the melting curve is found to be negative.
$Reason :$ Ice contracts on melting to water.