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 ............. $^oC$.

$A$ block of ice at temperature $-20^{\circ} C$ is slowly heated and converted to steam at $100^{\circ} C$. Which of the following diagrams is most appropriate?

Find the amount of heat supplied to decrease the volume of an ice-water mixture by $1 \, cm^3$ without any change in temperature. (Given: $\rho_{ice} = 0.9 \rho_{water}$,$L_{ice} = 80 \, cal/g$).

Two objects made of the same material have masses $m$ and $2m$ and are at temperatures $2T$ and $T$ respectively. When heat $Q$ is supplied to the object of mass $2m$, its temperature rises to $2T$. If the same heat $Q$ is supplied to the object of mass $m$, its temperature rises to:

$A$ metal block is made from a mixture of $2.4 \ kg$ of aluminium,$1.6 \ kg$ of brass,and $0.8 \ kg$ of copper. The metal block is initially at $20^{\circ} C$. If the heat supplied to the metal block is $44.4 \ cal$,find the final temperature of the block if the specific heats of aluminium,brass,and copper are $0.216, 0.0917, 0.0931 \ cal \cdot kg^{-1} \cdot ^{\circ}C^{-1}$ respectively. (in $^{\circ} C$)

$A$ 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: