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.