91.4k views
0 votes
A scuba diver takes a 2.8-L balloon from the surface, where the pressure is 1.0atm and the temperature is 34 C, to a depth of 25m, where the pressure is 3.5 ATM and the temperature is 18°C. What is the volume of the balloon at this depth

User Addmeaning
by
8.2k points

1 Answer

6 votes

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.

User Sweetie
by
7.4k points