$A$ 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 $= 0.91 \, J/g \cdot ^\circ C$]

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

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 $, J$)

The heat required to convert $8 \ g$ of ice at a temperature of $-20^{\circ}C$ to steam at $100^{\circ}C$ is (Specific heat capacity of ice $= 2100 \ J \ kg^{-1} \ K^{-1}$,specific heat capacity of water $= 4200 \ J \ kg^{-1} \ K^{-1}$,latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$ and latent heat of steam $= 2.268 \times 10^6 \ J \ kg^{-1}$) (in $kJ$)

The heat required to change $1 \,kg$ of ice at $-8^{\circ} C$ into water at $20^{\circ} C$ at $1 \,atm$ of pressure is closest to .............$\,kJ$. (Assume that ice has a specific heat capacity $2.1 \,kJ / kg \cdot K$,water has a specific heat capacity $4.2 \,kJ / kg \cdot K$,and the latent heat of fusion of ice is $333 \,kJ / kg$.)

The figure shows a glass tube (linear coefficient of expansion is $\alpha$) completely filled with a liquid of volume expansion coefficient $\gamma$. On heating,the length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$.