$A$ 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)

$A$ beaker is filled with water at $4\,^{\circ}C$. At one time the temperature is increased by a few degrees above $4\,^{\circ}C$ and at another time it is decreased by a few degrees below $4\,^{\circ}C$. One shall observe that:

The height of a waterfall is $84 \, m$. Assuming that the entire kinetic energy of falling water is converted into heat, the rise in temperature of the water will be $(g = 9.8 \, m/s^2, J = 4.2 \, J/cal, c = 1 \, cal/g^\circ C = 4200 \, J/kg^\circ C)$. (in $^\circ C$)

$10 \, g$ of ice at $0^{\circ} C$ is kept in a calorimeter of water equivalent $10 \, g$. How much heat (in $cal$) should be supplied to the apparatus to evaporate the water thus formed? (Neglect loss of heat)

How much thermal energy is required to change a $40 \ g$ ice cube from solid at $-10^{\circ} C$ to steam at $110^{\circ} C$ (in $kcal$)?
[Assume,latent heat of fusion for water $= 80 \ kcal/kg$,specific heat of water $= 1 \ kcal/kg^{\circ} C$,specific heat of ice $= 0.5 \ kcal/kg^{\circ} C$,specific heat of steam $= 0.48 \ kcal/kg^{\circ} C$,latent heat of vaporisation of water $= 540 \ kcal/kg$]

The height of Victoria Falls is $63 \ m$. What is the difference in temperature of water at the top and at the bottom of the fall? (In $^{\circ}C$)
[Given $1 \ cal = 4.2 \ J$ and specific heat of water $= 1 \ cal \ g^{-1} \ ^{\circ}C^{-1}$]