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According to Charles's law, for a fixed amount of gas at a constant pressure, the volume of the gas is directly proportional to its absolute temperature. The equation that represents this relationship is:

V₁ / T₁ = V₂ / T₂

Where: V₁ is the initial volume of the gas T₁ is the initial temperature of the gas in Kelvin V₂ is the final volume of the gas T₂ is the final temperature of the gas in Kelvin

To calculate the factor by which the volume increases, we can rearrange the equation:

V₂ = (V₁ * T₂) / T₁

Given that the gas is heated from 27 degrees Celsius to 627 degrees Celsius, we need to convert these temperatures to Kelvin:

T₁ = 27 + 273 = 300 K T₂ = 627 + 273 = 900 K

Assuming the pressure remains constant, we can substitute the values into the equation:

V₂ = (V₁ * 900) / 300

The factor by which the volume increases can be calculated as:

Factor = V₂ / V₁ = (V₁ * 900) / (V₁ * 300) = 900 / 300 = 3

Therefore, if the pressure remains constant, the volume of the gas will increase by a factor of 3 when heated from 27 degrees Celsius to 627 degrees Celsius.

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