$A$ metal ball immersed in alcohol weighs $W_1$ at $0^{\circ}C$ and $W_2$ at $50^{\circ}C$. The coefficient of cubical expansion of the metal $(\gamma)_m$ is less than that of alcohol $(\gamma)_{Al}$. Assuming that the density of the metal is large compared to that of alcohol,it can be shown that:

The thermo $e.m.f.$ of a thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700\,^{\circ}C$. If the cold junction is kept at $0\,^{\circ}C$,then the neutral temperature is:

$A$ bullet of mass $m$ moving with a uniform velocity $v$ stops suddenly after hitting a target. If the whole mass melts,given the specific heat $S$,initial temperature $25^{\circ}C$,melting point $475^{\circ}C$,and latent heat $L$,then $v$ is given by:

Water falls from a height of $200 \ m$ into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. ($g = 10 \ m/s^2$,specific heat of water $s = 4200 \ J/(kg \ K)$) (in $K$)

An iron rod of heat capacity $C$ is heated to temperature $8T_0$. It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as a diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$. The cylinder with the piston combined have a heat capacity $2C$. Find the equilibrium temperature. (Assume the temperature of air to be uniform and equal to the vessel at all times).

In a thermocouple,if the thermo $EMF$ is given by $E = 40\theta - \frac{\theta^2}{20}$,then the neutral temperature will be .......... $^oC$.