$A$ lead bullet of $20 \ g$ travelling at $300 \ m/s$ strikes against a block of wood and comes to rest. Assuming $50 \%$ of heat is absorbed by the bullet,the increase in its temperature is $.....^{\circ} C$ (take specific heat of lead $= 150 \ J/kg \cdot K$).

$A$ clock pendulum having a coefficient of linear expansion $\alpha = 9 \times 10^{-7} /^{\circ}C$ has a period of $0.5 \ s$ at $20^{\circ}C$. If the clock is used in a climate where the temperature is $30^{\circ}C$,how much time does the clock lose in each oscillation? (Assume $g$ is constant)

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 $\alpha$.

$A$ steel pendulum clock manufactured at $32^{\circ} C$ and working at $47^{\circ} C$ is nearly (Coefficient of linear expansion of steel $= 12 \times 10^{-6} /{ }^{\circ} C$)

If in the winter season the surface temperature of a lake is $1^{\circ} C$,the temperature at the bottom of the lake will be ............

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 $333 \,kJ / kg$.)