Two substances $A$ and $B$ of the same mass are heated at a constant rate. The variation of temperature $\theta$ of the substances with time $t$ is shown in the figure. Choose the correct statement.

The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}$ $(r_{1} = 1.5 r_{2})$ through $1 \ K$ are in the ratio of:

The factor not needed to calculate heat lost or gained when there is no change of state is

Which of the substances $A, B$,or $C$ has the highest specific heat? The temperature-time graph is shown.

$A$ current-carrying wire heats a metal rod. The wire provides a constant power $(P)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $(T)$ in the metal rod changes with time $(t)$ as:
$T(t) = T_0(1 + \beta t^{1/4})$
where $\beta$ is a constant with appropriate dimensions,while $T_0$ is a constant with the dimension of temperature. The heat capacity of the metal is:

The temperature of $5$ moles of a gas at constant volume is changed from $100^{\circ} C$ to $120^{\circ} C$. The change in internal energy is $80 \,J$. The total heat capacity of the gas at constant volume in $J/K$ is: