A beaker contains $200\, gm$ of water. The heat capacity of the beaker is equal to that of $20\, gm$ of water. The initial temperature of water in the beaker is $20°C.$ If $440\, gm$ of hot water at $92°C$ is poured in it, the final temperature (neglecting radiation loss) will be nearest to........ $^oC$

$1 \,kg$ of ice at $-20^{\circ} C$ is mixed with $2 \,kg$ of water at $90^{\circ} C$. Assuming that there is no loss of energy to the environment, the final temperature of the mixture is ............ $^{\circ} C$ (Assume, latent heat of ice $=334.4 \,kJ / kg$, specific heat of water and ice are $4.18 \,kJ kg ^{-1} K ^{-1}$ and $2.09 \,kJ kg ^{-1}- K ^{-1}$, respectively.)

In the definition of 'calorie' one calorie is the heat required to raise the temperature of $1\  gram$ of water through $1\  ^oC$ in a certain interval of temperature. The temperature interval is

A steam engine intakes $50\, g$ of steam at $100^{\circ} C$ per minute and cools it down to $20^{\circ} C$. If latent heat of vaporization of steam is $540 \,cal g ^{-1}$, then the heat rejected by the steam engine per minute is .........$\times 10^{3}$$cal.$

$100\,g$ of water is supercooled to $-\,10\,^oC$. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze ? $[S_W = 1\,cal\,g^{-1}\,^oC^{-1}$ and ${L^W}_{{\text{fussion}}}$ $= 80\,cal\,g^{-1}]$

A vessel contains $110\, g$ of water. The heat capacity of the vessel is equal to $10\, g$ of water. The initial temperature of water in vessel is $10°C.$ If $220\, g$ of hot water at $70°C$ is poured in the vessel, the final temperature neglecting radiation loss, will be........ $^oC$