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 ............

If the $emf$ of a thermocouple,one junction of which is kept at $0\,^{\circ}C$,is given by $e = at + 1/2\,bt^2$,then the neutral temperature will be

$A$ 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 thermo $e.m.f.$ produced in a thermocouple is given by the equation $E = 40\theta - \frac{\theta^2}{20}$,where $\theta$ is the temperature difference between the two junctions. The neutral temperature is ............. $^oC$.

Consider a rectangular sheet of solid material of length $l=9 \ cm$ and width $d=4 \ cm$. The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \ K^{-1}$ at room temperature and one atmospheric pressure. The mass of the sheet is $m=0.1 \ kg$ and the specific heat capacity is $C_v=900 \ J \ kg^{-1} K^{-1}$. If the amount of heat supplied to the material is $8.1 \times 10^2 \ J$,then the change in area of the rectangular sheet is:

If $60 \%$ of the kinetic energy of water falling from a $210 \ m$ high waterfall is converted into heat,the rise in temperature of the water at the bottom of the fall is nearly (specific heat of water $= 4.2 \times 10^3 \ J \ kg^{-1} \ K^{-1}$ and $g = 10 \ m/s^2$):