The cubic expansivity of a certain gas at constant pressure is \(\frac{1}{273} k^{-1}\). If a given mass of the gas is held at constant pressure and its vol...

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The cubic expansivity of a gas at constant pressure is defined as the fractional increase in volume per degree rise in temperature. Let the volume of the gas at 0°C be V₀ and the temperature at which we need to find the volume of the gas be T₁. The increase in temperature = T₁ - 0 = T₁. The fractional increase in volume = cubic expansivity x increase in temperature = \(\frac{1}{273}\) x T₁. The increase in volume = V₀ x fractional increase in volume = V₀ x \(\frac{1}{273}\) x T₁. The final volume of the gas at T₁ = V₀ + increase in volume = V₀ + V₀ x \(\frac{1}{273}\) x T₁ = V₀(1 + \(\frac{1}{273}\) x T₁). Substituting the given values, we get: Volume at 273^oC = 273m³(1 + \(\frac{1}{273}\) x 273) = 546m³. Therefore, the volume of the gas at 273^oC is 546m³. The correct option is (b).