How much energy in $kJ$ is required to heat $5 \, kg$ of water from $20^oC$ to its boiling point? (Specific heat of water = $4.2 \, kJ \, kg^{-1} \, ^oC^{-1}$)

$A$ heater supplying constant power $P$ watts is switched $ON$ at time $t=0$ 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,

The density of a material $A$ is $1500 \ kg/m^3$ and that of another material $B$ is $2000 \ kg/m^3$. It is found that the heat capacity of $8$ volumes of $A$ is equal to the heat capacity of $12$ volumes of $B$. The ratio of specific heats of $A$ and $B$ will be

At which temperature is the specific heat of water minimum (in $^\circ C$)?

Three bodies $A, B$ and $C$ of masses $m, m$ and $\sqrt{3}m$ respectively are supplied heat at a constant rate. The change in temperature $\theta$ versus time $t$ graph for $A, B$ and $C$ are shown by $I, II$ and $III$ respectively. If their specific heat capacities are $S_A, S_B$ and $S_C$ respectively,then which of the following relations is correct? (Initial temperature of body is $0\,^{\circ}C$)

The specific heat capacity of a substance is temperature dependent and is given by the formula $C = kT$,where $k$ is a constant of suitable dimensions in $SI$ units,and $T$ is the absolute temperature. If the heat required to raise the temperature of $1 \ kg$ of the substance from $-73^{\circ} C$ to $27^{\circ} C$ is $nk$,the value of $n$ is. . . . . . [Given: $0 \ K = -273^{\circ} C$.]