Question

The specific heat at constant volume is
(A) any of the above
(B) the amount of heat required to raise the temperature of 1kg water through 1 degree
(C) the amount of heat required to raise the temperature of a unit mass of gas through 1 degree at constant volume
(D) the amount of heat required to raise the temperature of a unit mass of gas through 1 degree at constant pressure

Answer 1

Hint: Heat is a form of energy and is related to temperature as it has the capacity to raise the temperature of a body when it is supplied to that body. Also, the heat has the same effect on any form of matter, be it solid, liquid or a gas. It will cause the temperature to rise in all objects.

Complete step by step solution:
-Heat transfer is the process of exchange of heat from 1 system to another. It can be done by conduction, convection or radiation. Conduction basically occurs in solids, convection in liquids and radiation in a vacuum.
-To be able to solve the question, we must know total heat capacity, molar heat capacity and specific heat capacity of a substance.
Heat capacity is the heat needed to raise the temperature of a system by ${{1}^{\circ }}C$ under a given process. It is represented mathematically as ${{C}_{T}}=\dfrac{dq}{dT}J{{/}^{\circ }}C$ .
Molar heat capacity is the heat required to raise the temperature of 1 mole of a substance by unit degree. It is represented as $C=\dfrac{dq}{ndT}J/mol/K$.
Specific heat capacity is the heat required to raise the temperature of a unit mass of a substance by unit degree temperature. It is represented mathematically as $s=\dfrac{dq}{mdT}J/g/K$.
-In the question, we are asked about the specific heat at constant volume. So the answer is either C or D. We know that the heat capacity is the heat needed to raise the temperature of a system by ${{1}^{\circ }}C$.
-If the heat capacity is found at a constant volume, then it becomes the amount of heat required to raise the temperature of a unit mass of gas through 1 degree at constant volume. If it is found at constant pressure, then it becomes the amount of heat required to raise the temperature of a unit mass of gas through 1 degree at constant pressure.
-The specific heat at constant volume and at constant pressure is denoted by different abbreviations and can be given as
$\begin{align}
& Q=n{{C}_{V}}\Delta T\text{ }\left( for\text{ }cons\text{tant volume} \right) \\
& \text{Q=n}{{\text{C}}_{P}}\Delta T\text{ }\left( for\text{ constant pressure} \right) \\
\end{align}$

Therefore the correct option is (C).

Note: For an ideal gas, the specific heat can be written in the form
$Q=n{{C}_{V}}\Delta T=\dfrac{3}{2}nR\Delta T$
This means that we can relate the constants R and ${{C}_{V}}$ and their relation is
${{C}_{V}}$ $=1.5R$