Answer:
Step-by-step explanation:
AI-generated answer
To find the volume of the balloon at a depth of 25m, we need to use the combined gas law, which relates the initial and final pressure, volume, and temperature of a gas.
1. Convert the temperatures from Celsius to Kelvin:
- Initial temperature: 34°C + 273.15 = 307.15 K
- Final temperature: 18°C + 273.15 = 291.15 K
2. Convert the depth from meters to atmospheres (atm):
- Pressure at the surface: 1.0 atm
- Pressure at a depth of 25m: 3.5 atm
3. Apply the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
- P1 and P2 are the initial and final pressures (in atm)
- V1 is the initial volume (2.8 L)
- T1 and T2 are the initial and final temperatures (in Kelvin)
- V2 is the volume we want to find
4. Plug in the given values into the equation and solve for V2:
(1.0 atm * 2.8 L) / (307.15 K) = (3.5 atm * V2) / (291.15 K)
Cross-multiply and solve for V2:
2.8 L * 3.5 atm * 291.15 K = 1.0 atm * V2 * 307.15 K
2.8 L * 3.5 atm * 291.15 K / 307.15 K = V2
Calculate V2:
V2 = 2.65 L
Therefore, the volume of the balloon at a depth of 25m is approximately 2.65 liters.