A heater supplying constant power $P$ watts is switched $ON$ at time $t=0 \,min$ to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid $T(t)$ at equal time intervals. A graph is plotted with $T(t)$ on the $Y$-axis versus $t$ on the $X$-axis. Assume that there is no heat loss to the surroundings during heating. Then,

One kilogram of ice at $0°C$ is mixed with one kilogram of water at $80°C.$ The final temperature of the mixture is…….. $^oC$

$($Take : specific heat of water$ = 4200\,J\,k{g^{ – 1}}\,{K^{ – 1}}$, latent heat of ice $ = 336\,kJ\,k{g^{ – 1}})$

A lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it, the initial speed of bullet is ………… $ms ^{-1}$

(Given, initial temperature of the bullet $=127^{\circ} C$,

Melting point of the bullet $=327^{\circ} C$,

Latent heat of fusion of lead $=2.5 \times 10^{4} \,J Kg ^{-1}$,

Specific heat capacity of lead $=125 \,J / kg K$ )

Ice in a freezer is at $-7^{\circ} C .100 \,g$ of this ice is mixed with $200 \,g$ of water at $15^{\circ} C$. Take the freezing temperature of water to be $0^{\circ} C$, the specific heat of ice equal to $2.2 \,J / g { }^{\circ} C$, specific heat of water equal to $4.2 \,J / g ^{\circ} C$ and the latent heat of ice equal to $335 \,J / g$. Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to ………. $g$

What is calorimetry ? What is calorimeter ? Explain its principle and construction.