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Charles’ law is represented mathematically as,
A) ${{V}_{t}}=K{{V}_{o}}t$
C)${{V}_{t}}={{V}_{o}}\left( 1+\dfrac{273}{t} \right)$
D) ${{V}_{t}}={{V}_{o}}\left( 1+\dfrac{t}{273} \right)$

Last updated date: 13th Jun 2024
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Hint: The answer to this question lies in the fact that Charles’ law is given by the formula which is based on the constant pressure, the volume of ideal gas is directly proportional to its absolute temperature that is $V\propto t$

Complete step by step solution:
From the lower classes of chemistry, we have come across the concepts in the physical chemistry about the kinetic theory of gases.
- One among those is the Charles’ law which states that “The volume of a fixed mass of the gas decreases or even increases by $\dfrac{1}{273}$times that of the volume of that particular gas at ${{0}^{0}}C$for every fall or rise in temperature of the liquid by ${{1}^{0}}C$“.
- This means that if we denote decrease of temperature as ‘t’ then the decrease is $\dfrac{t}{273}$and the volume at ${{0}^{0}}C$as${{V}_{0}}$then according to the definition if we increase temperature by ${{t}^{0}}C$for every rise or fall in temperature by ${{V}_{0}}$ times can be given as,
\[{{V}_{0}}+\dfrac{{{V}_{o}}\times t}{273}\]
By solving this equation we have,
\[{{V}_{0}}\left( 1+\dfrac{t}{273} \right)={{V}_{t}}\]
Where ${{V}_{t}}$= rise in temperature that is final temperature.

Thus, the correct answer is option D) ${{V}_{t}}={{V}_{o}}\left( 1+\dfrac{t}{273} \right)$

Additional information:
Charles’ law is the statement which says that at constant pressure the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature. This is a special case of the general gas law and can be derived from the kinetic theory of gases under the assumption of an ideal gas or perfect gas.

Note: Sometimes confusions may occur between the definitions of Charles’ law and Boyle’s law. Note that Charles’ law gives relationship between volume and temperature at constant pressure and Boyle’s law gives relationship between volume and pressure at constant temperature.