The variation of density of water with temperature is represented by the

$A$ thermally insulated vessel contains $150\, g$ of water at $0\, ^oC$. Then the air from the vessel is pumped out adiabatically. $A$ fraction of water turns into ice and the rest evaporates at $0\, ^oC$ itself. The mass of evaporated water will be closest to ....... $g$ (Latent heat of vaporization of water $= 2.10 \times 10^6\, J/kg$ and Latent heat of fusion of water $= 3.36 \times 10^5\, J/kg$).

$A$ bullet of mass $5\, g$,travelling with a speed of $210\, m/s$,strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $0.030\, cal/(g \cdot ^{\circ}C)$ $(1\, cal = 4.2 \times 10^{7}\, ergs)$ is close to $.......^{\circ}C$.

Calculate the amount of heat (in calories) required to convert $5\,g$ of ice at $0^{\circ}C$ to steam at $100^{\circ}C$.

$A$ continuous flow water heater (geyser) has an electrical power rating $= 2 \, kW$ and efficiency of conversion of electrical power into heat $= 80 \%$. If water is flowing through the device at the rate of $100 \, cc/sec$,and the inlet temperature is $10^{\circ} C$,the outlet temperature will be ....... $^{\circ} C$.

$A$ 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)