If there are no heat losses,the heat released by the condensation of $x \, g$ of steam at $100^\circ C$ into water at $100^\circ C$ can be used to convert $y \, g$ of ice at $0^\circ C$ into water at $100^\circ C$. Then the ratio $y : x$ is nearly (in $:1$)

The pressure applied from all directions on a cube is $P$. How much should its temperature be raised to maintain the original volume? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$.

It is possible for a substance to coexist in all three phases in equilibrium,when the substance is at

The heat extracted out of $x \ \text{g}$ of water initially at $50^\circ \text{C}$ to cool it down to $0^\circ \text{C}$ is sufficient to evaporate $(1000 - x) \ \text{g}$ of water also initially at $50^\circ \text{C}$. The value of $x$ (closest integer) is . . . . . . . (Take latent heat of water $L = 2256 \ \text{kJ/kg}$, specific heat capacity of water $c = 4200 \ \text{J/kg}\cdot \text{K}$)

Water falls from a height of $200 \ m$ into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. ($g = 10 \ m/s^2$,specific heat of water $s = 4200 \ J/(kg \ K)$) (in $K$)

$A$ drilling machine of $10 \, kW$ power is used to drill a bore in a small aluminium block of mass $8 \, kg$. If $50 \%$ of power is used up in heating the machine itself or lost to the surroundings,then the rise in temperature of the block in $2.5 \, minutes$ is ........ $^\circ C$. [Specific heat of aluminium $= 0.91 \, J/g \cdot ^\circ C$]