Understanding the Concept
This problem utilizes Charles's Law, which states that the volume of an ideal gas is directly proportional to its absolute temperature when the pressure is held constant.
Formula
Charles's Law can be expressed as:
V₁/T₁ = V₂/T₂
where:
* V₁ = Initial volume
* T₁ = Initial temperature (in Kelvin)
* V₂ = Final volume
* T₂ = Final temperature (in Kelvin)
Calculations
1. Convert Temperatures to Kelvin:
* T₁ = 273 K (already in Kelvin)
* T₂ = 373 K
2. Find the Ratio of Temperatures:
* T₂/T₁ = 373 K / 273 K = 1.36
3. Determine the Final Volume:
* Since the volume is directly proportional to the temperature, the final volume will be 1.36 times the initial volume.
* To find the final volume (V₂), we need the initial volume (V₁). We know the radius of the balloon is 10 cm. Let's calculate the initial volume:
* V₁ = (4/3)πr³ = (4/3) * π * (10 cm)³ = 4188.79 cm³ (approximately)
4. Calculate the Final Volume:
* V₂ = V₁ * (T₂/T₁) = 4188.79 cm³ * 1.36 = 5704.25 cm³ (approximately)
Answer
The volume of the round balloon at 373 K will be approximately 5704.25 cm³.
