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