Assertion :Volume: temperature ratio is constant for a fixed amount of gas at constant pressure. Reason: At constant pressure the volume of a given mass of a gas increases or decreases by $1 / 273$ of its volume at $0^{o} C$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
According to Charle's law: $V \propto T$ at constant pressure for a fixed amount of gas.
Therefore, assertion is correct.
$T_{1} = 0 ℃ = 273 K ⟹ \frac{V_{2}}{V_{1}} = \frac{T_{2}}{T_{1}} ⟹ \frac{V_{2}}{V_{1}} = T_{2} \times \frac{1}{273}$
Therefore, reason is correct.
Reason is the correct explanation of assertion.
Since Charle's law states that for every 1℃ increase in temperature of a gas, the volume increases by $\frac{1}{273}$ of the original volume at constant pressure.
For example,
$T_{1} = 273 K T_{2} = 274 K ∴ \frac{T_{2}}{T_{1}} = \frac{274 K}{273 K} ⟹ \frac{V_{2}}{V_{1}} = \frac{274 \times V_{1}}{273} = (1 + \frac{1}{273}) V_{1}$

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Assertion :Volume: temperature ratio is constant for a fixed amount of gas at constant pressure. Reason: At constant pressure the volume of a given mass of a gas increases or decreases by 1/273 of its volume at 0oC

Assertion :Volume: temperature ratio is constant for a fixed amount of gas at constant pressure. Reason: At constant pressure the volume of a given mass of a gas increases or decreases by $1 / 273$ of its volume at $0^{o} C$