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 .......... $J/K$

Three liquids with masses ${m_1},\,{m_2},\,{m_3}$ are thoroughly mixed. If their specific heats are ${c_1},\,{c_2},\,{c_3}$ and their temperatures ${T_1},\,{T_2},\,{T_3}$ respectively, then the temperature of the mixture is

A kettle with $2\, littre$ water at $27\,^oC$ is heated by operating coil heater of power $1\, kW$. The heat is lost to the atmosphere at constant rate $160\, J/sec$, when its lid is open. In how much time will water heated to $77\,^oC$. (specific heat of water $= 4.2\, kJ/kg$) with the lid open ?

$100\,g$ 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 mass of material exists in its solid format its melting temperature $0\,^o  C$. The following processes then occur to the material

Process $-1$:An amount of thermal energy $Q$ is added to the material and $\frac{2}{3}$ of the material melts.

Process $-2$:An identical additional amountof thermal energy $Q$ is added to the materlal is now a liquid at $4\,^o C$

........ $^oC$ is the ratio of the latent heat of fusion to the specific heat of the liquid for this material.

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