If you have 8.3 liters of air in a balloon at room temperature (26°C) and heat the balloon to 38°C, what would the new volume be?
V1/T1 = V2/T2
T1 and T2 must be in Kelvin.
i got 8.3/299.15 = v2/311.15
but how do i get v2?
If you put this on a piece of paper, more or less like this, then cross multiply. (Ignore the .....those are just there for spacing since we can't space on the boards.)
8.3.......V2
------- = ----
299.15.....311.15
Cross multiply and you have
299.15 x V2 = 8.3 x 311.15
Then solve for V2.
To answer this question, we need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, as long as the pressure remains constant.
Here's how you can solve it step by step:
1. Convert the temperatures from Celsius to Kelvin:
- Initial temperature (T1) = 26°C + 273.15 = 299.15 K
- Final temperature (T2) = 38°C + 273.15 = 311.15 K
2. Use the formula for Charles's Law: V1/T1 = V2/T2, where V1 is the initial volume, V2 is the final volume, T1 is the initial temperature, and T2 is the final temperature.
Rearrange the formula to solve for V2 (the final volume):
V2 = (V1 * T2) / T1
3. Substitute the given values into the equation:
V2 = (8.3 L * 311.15 K) / 299.15 K
4. Calculate the final volume:
V2 = 8.638 L (rounded to three decimal places)
Therefore, the new volume of the balloon at 38°C would be approximately 8.638 liters.