If the ratio of the diameters of two spheres made of the same material is $1:2$,what is the ratio of their heat capacities?

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

The molar mass of a substance is $50 \, g/mol$. When $300 \, J$ of heat is supplied to a $25 \, g$ sample of this substance,its temperature increases from $30^{\circ}C$ to $50^{\circ}C$. The value of its molar heat capacity is ..... $J/mol \cdot ^{\circ}C$.

Heat given to a body which raises its temperature by $1\ ^oC$ is

The figure below shows the variation of specific heat capacity $(C)$ of a solid as a function of temperature $(T)$. The temperature is increased continuously from $0$ to $500 \ K$ at a constant rate. Ignoring any volume change,which of the following statement$(s)$ is (are) correct to a reasonable approximation?
$(A)$ The rate at which heat is absorbed in the range $0-100 \ K$ varies linearly with temperature $T$.
$(B)$ Heat absorbed in increasing the temperature from $0-100 \ K$ is less than the heat required for increasing the temperature from $400-500 \ K$.
$(C)$ There is no change in the rate of heat absorption in the range $400-500 \ K$.
$(D)$ The rate of heat absorption increases in the range $200-300 \ K$.

$A$ 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,