To determine the factor by which the volume changes when the temperature of a gas is changed at constant pressure, we can use Charles's law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure.
Charles's law can be expressed mathematically as:
V₁ / T₁ = V₂ / T₂
Where: V₁ is the initial volume, T₁ is the initial temperature, V₂ is the final volume, and T₂ is the final temperature.
In this case, the initial temperature is 50°C (or 50 + 273.15 Kelvin) and the final temperature is 100°C (or 100 + 273.15 Kelvin). Let's assume the initial volume is represented by V₁, and we want to find the factor by which the volume changes, which is V₂ / V₁.
Substituting the values into Charles's law equation:
V₁ / (50 + 273.15) = V₂ / (100 + 273.15)
We can now solve for V₂ / V₁:
V₂ / V₁ = (100 + 273.15) / (50 + 273.15)
Calculating the right side of the equation:
V₂ / V₁ = 373.15 / 323.15 ≈ 1.154
Therefore, the volume changes by a factor of approximately 1.154 (or 15.4%).