By what property can the temperature difference be determined if the state of a substance does not change during the absorption of a given amount of heat?

Why is water used as a coolant in automobile radiators?

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:

Derive the equation for the molar specific heat capacity of solids.

The specific heat $C$ of a solid at low temperature shows temperature dependence according to the relation $C = D T^{3}$, where $D$ is a constant and $T$ is the temperature in Kelvin. $A$ piece of this solid of mass $m \ kg$ is taken and its temperature is raised from $20 \ K$ to $30 \ K$. The amount of heat required in the process in energy units is

$A$ 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,