Final answer:
The volume of the weather balloon at altitude, with a pressure change from 740 mmHg to 385 mmHg and a temperature change from 32.4°C to -13.1°C, is approximately 47.93 L.
Step-by-step explanation:
To calculate the new volume of a weather balloon using the ideal gas law when pressure and temperature change, the combined gas law is applied:
P1 × V1 / T1 = P2 × V2 / T2
Where P stands for pressure, V for volume, and T for temperature in Kelvin. Initially, the balloon has a volume of 27.6 L at a pressure of 740 mmHg and a temperature of 32.4°C. At altitude, the pressure is 385 mmHg and the temperature is -13.1°C. First, convert temperatures to Kelvin:
- T1 = 32.4 + 273.15 = 305.55 K
- T2 = -13.1 + 273.15 = 260.05 K
Using the combined gas law, solving for V2 gives:
V2 = (P1 × V1 × T2) / (P2 × T1)
V2 = (740 mmHg × 27.6 L × 260.05 K) / (385 mmHg × 305.55 K)
V2 = 47.93 L
The balloon will thus expand to a volume of approximately 47.93 L at the altitude conditions given.