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...
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 volume at 0oC is 273m3, determine the volume of the gas at 273oC.
Answer Details
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 273oC = 273m3(1 + \(\frac{1}{273}\) x 273) = 546m3. Therefore, the volume of the gas at 273oC is 546m3. The correct option is (b).