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 $10\,^oC.$  If  $220\,\,g$  of hot water at  $70\,^oC$ is poured in the vessel, the final temperature neglecting radiation loss, will be …….. $^oC$

The water equivalent of $20 \,g$ of aluminium (specific heat $0.2 \,cal ^{-1}{ }^{\circ} C ^{-1}$ ), is ……… $g$

A piece of ice (heat capacity $=2100 \mathrm{~J} \mathrm{~kg}^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat $=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$ ) of mass $\mathrm{m}$ grams is at $-5^{\circ} \mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{~J}$ of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that $1 \ \mathrm{gm}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

A calorimeter contains $0.2\, kg$ of water at $30\,^oC$, $0.1\,kg$ of water at $60\,^oC$ is added to it, the mixture is well stirred and the resulting temperature is found to be $35\,^oC$. The thermal capacity of calorimeter is ………. $J/K$

The specific heat of alcohol is about half that of water. Suppose you have identical masses of alcohol and water. The alcohol is initially at temperature $T_A$ . The water is initially at a different temperature $T_W$ . Now the two fluids are mixed in the same container and allowed to come into thermal equilibrium, with no loss of heat to the surroundings. The final temperature of the mixture will be