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

$A$ steel ball of mass $200 \,g$ falls freely from a height of $20 \,m$ and bounces to a height of $10.8 \,m$ from the ground. If the energy lost in this process is absorbed by the ball, the rise in its temperature is ($g = 10 \,ms^{-2}$, specific heat capacity of steel is $460 \,Jkg^{-1} K^{-1}$). (in $^{\circ} C$)

$A$ hammer of mass $200 \ kg$ strikes a steel block of mass $200 \ g$ with a velocity $8 \ ms^{-1}$. If $23 \%$ of the energy is utilized to heat the steel block,the rise in temperature of the block is (specific heat capacity of steel,$s = 460 \ J \ kg^{-1} \ K^{-1}$) (in $K$)

How much energy will be released by cooling $1\,kg$ of water up to a temperature of $10\,^{\circ}C$?

$A$ thin-walled cylindrical metal vessel with a linear coefficient of expansion $10^{-3} \ ^\circ C^{-1}$ contains benzene with a volume expansion coefficient of $10^{-3} \ ^\circ C^{-1}$. If the vessel and its contents are heated by $10 \ ^\circ C$,the pressure due to the liquid at the bottom:

Water falls from a height of $500 \ m$. What is the rise in temperature of water at the bottom if the whole energy remains in the water? (Assume $g = 9.8 \ m/s^2$ and specific heat capacity of water $c = 4200 \ J/kg \cdot ^\circ C$)