Question

Heat capacity has SI unit as $J{K^{ - 1}}$

A. True

B. False

Answer 1

Hint: From the definition of heat capacity we can determine its SI unit. Heat capacity is slightly different from specific heat capacity which is defined as heat capacity per unit mass.

Formula used

$c = \dfrac{{dQ}}{{dT}}$ where $dQ$ is the amount of heat required to raise the temperature of a body by an amount of $dT$.

Complete step by step solution

Heat Capacity or thermal capacity is defined as the amount of energy required to raise the mass of a substance by unit degree temperature.

Now, we know that the SI unit of energy is joule which is symbolized by $J$ and the SI unit of temperature is kelvin symbolized by $K$.

As, heat capacity is given as heat energy per unit temperature, so its unit must be $J{K^{ - 1}}$

From a thermodynamic point of view, we can express the heat capacity in a number of ways.

Usually it is defined as $c = \dfrac{{dQ}}{{dT}}$ where $dQ$ is the amount of heat required to raise the temperature of a body by an amount of $dT$.

According to the first law of thermodynamics, if heat is supplied to a system at constant pressure for one mole of gas, it is represented as ${C_P}$.

If heat is supplied to the system at constant volume then, it is represented as ${C_V}$

The internal energy of a one mole of a  thermodynamic system can be given by,

$dU = {C_V}dT$

So, the correct answer is “Option A”.

Note: For a gas, the ratio of heat capacities $\dfrac{{{C_P}}}{{{C_V}}} = \gamma $ can be used to determine its degree of freedom. Degrees of freedom of a system is defined as the minimum number of coordinates required to specify the position and configuration of a dynamical system in space.