Final answer:
The volume of the helium-filled balloon at a height of 36 km, under the conditions given, can be calculated using the Combined Gas Law, and it is approximately 9.47 × 10^7 liters.
Step-by-step explanation:
To calculate the volume of the helium-filled balloon at a height of 36 km, where the pressure is 73.0 mmHg and the temperature is 235.0 K, we can use the Combined Gas Law. This law combines the three gas laws: Boyle's Law, Charles's Law, and Gay-Lussac's Law. It is represented by the formula:
P1 * V1 / T1 = P2 * V2 / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature (in Kelvin)
P2 = final pressure
V2 = final volume (unknown)
T2 = final temperature (in Kelvin)
To apply the Combined Gas Law to our scenario, we must first convert the initial temperature to Kelvin:
T1 = 27.8°C + 273.15 = 300.95 K
Now we can plug in the values:
(752 mmHg * 9.47 × 10^4 L) / 300.95 K = (73.0 mmHg * V2) / 235.0 K
By rearranging the formula to solve for V2, the final volume, we get:
V2 = (752 mmHg * 9.47 × 10^4 L * 235.0 K) / (73.0 mmHg * 300.95 K)
After performing the calculations:
V2 = 9.47 × 10^7 L approximately (the exact answer depends on the precision of the calculations and the rounding)
Thus, the volume of the balloon at 36 km would be approximately 9.47 × 10^7 liters.