Question

Which of the following statements does not describe Charles’ law?
A. The volume of a given amount of a gas at constant pressure varies directly as its absolute temperature
B. For each degree change in temperature, the volume of a sample of a gas changes by the fraction $\dfrac{1}{273}$of its volume at ${{0}^{\circ }}C$
C. All gases expand or contract by the same fraction of their volume at ${{0}^{\circ }}C$per degree change in temperature.
D. ${{V}_{1}}={{V}_{\circ }}\left( \dfrac{273-1}{273} \right)$

Answer 1

Hint: As we know that Charles law is used to explain the effects of temperature on gases under constant pressure. According to Charles law:
\[\begin{align}
& V\propto T \\
& \dfrac{V}{T}=k \\
\end{align}\]
Where, V= volume of the gas, T= temperature of the gas, in kelvin, K= constant

Complete Step by step solution:
- As we know that according to Charles law, at a constant pressure the volume of a given amount of gas is directly proportional to its absolute temperature. It is found that at ${{0}^{\circ }}C$ per degree changes in temperature, all gases contract or we can say expand by same fraction of their volumes
As temperature is directly proportional to volume, we can write the expression for this mathematically as:
\[\begin{align}
& V\propto T \\
& \dfrac{V}{T}=k \\
\end{align}\]
Where,
V= volume of the gas
T= temperature of the gas, in kelvin
K= constant
For each degree change in temperature, the volume of a sample of a gas changes by the fraction $\dfrac{1}{273}$of its volume at ${{0}^{\circ }}C$, therefore we can write:
${{V}_{T}}={{V}_{\circ }}+\left( \dfrac{1}{273}\times {{V}_{\circ }} \right)\times T$
${{V}_{T}}={{V}_{\circ }}+\left( 1+{{\dfrac{T}{273}}_{\circ }} \right)$
Where,
${{V}_{T}}$ = volume of gas at temperature T
${{V}_{\circ }}$ = volume of gas at${{0}^{\circ }}C$

- Hence, we can conclude that the correct option is (d), that is ${{V}_{1}}={{V}_{\circ }}\left( \dfrac{273-1}{273} \right)$does not describe Charles’ law.

Note: - We must note here that Charles law is applicable for real gases only at low pressures and high temperatures. And is only applicable to real gases.
- We can see that at high pressure, the relation between temperature and volume is not linear.