By what factor does the volume increase when An ideal gas is allowed to expand from 3.80 L to 32.3 L at constant temperature
32.3/3.80 = ?
To determine the factor by which the volume increases when an ideal gas expands at constant temperature, we can use the relationship known as Boyle's Law, which states that the product of the initial volume and pressure is equal to the product of the final volume and pressure for a given amount of gas at constant temperature.
Mathematically, Boyle's Law can be represented as:
P₁V₁ = P₂V₂
Where:
P₁ and P₂ are the initial and final pressures, respectively.
V₁ and V₂ are the initial and final volumes, respectively.
In this case, the constant temperature means that the initial and final temperatures remain the same.
Given:
Initial Volume (V₁) = 3.80 L
Final Volume (V₂) = 32.3 L
Since the temperature remains constant, we can assume that the initial pressure (P₁) is equal to the final pressure (P₂). Hence, our equation simplifies to:
V₁ = V₂
Now, let's plug in the values:
3.80 L = 32.3 L
To find the factor by which the volume increases, divide the final volume by the initial volume:
Factor = V₂ / V₁ = 32.3 L / 3.80 L ≈ 8.50
Therefore, the volume increases by a factor of approximately 8.50.
To determine the factor by which the volume increases, you need to calculate the ratio of the final volume to the initial volume.
The formula for the factor by which a quantity increases is:
Factor = final value / initial value
In this case, the initial volume is given as 3.80 L, and the final volume is given as 32.3 L. Therefore, you can calculate the factor as follows:
Factor = 32.3 L / 3.80 L
Now, let's do the math:
Factor = 8.5
So, the factor by which the volume increases when the ideal gas expands from 3.80 L to 32.3 L at constant temperature is 8.5.