Final answer:
Using the combined gas law, the volume of the high altitude balloon at a height of 20 km, where the temperature is -48 °C and the pressure is 63.1 torr, is found to be approximately 12,300 L; the correct answer is (d) 12,300 L.
Step-by-step explanation:
The student's question involves calculating the volume of a high altitude balloon at varying conditions using the combined gas law. The combined gas law relates pressure, volume, and temperature of a gas, and it can be stated as (P1 × V1) / T1 = (P2 × V2) / T2 where P is pressure, V is volume, and T is temperature (in Kelvins).
To solve the problem, convert all units to standard units first:
21°C + 273.15 = 294.15K (-48°C + 273.15 = 225.15K), and convert torr to atmospheres by dividing by 760.
- Initial conditions (at ground level): P1 = 745 torr (0.981 atm), V1 = 1.41 × 10^4 L, T1 = 294.15 K
- Final conditions (at altitude): P2 = 63.1 torr (0.083 atm), T2 = 225.15 K
Using the combined gas law, solve for V2:
(0.981 atm × 1.41 × 10^4 L) / 294.15 K = (0.083 atm × V2) / 225.15 K
V2 = (0.981 atm × 1.41 × 10^4 L × 225.15 K) / (294.15 K × 0.083 atm)
V2 ≈ 12,300 L
Therefore, the correct answer is (d) 12,300 L.