A weather balloon is inflated to a volume of 29.9 L at a pressure of 755 mmHg and a temperature of 33.0 ∘C. The balloon rises in the atmosphere to an altitude where the pressure is 385 mmHg and the temperature is -16.2 ∘C.
Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.
To solve this problem, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (755 mmHg)
V1 = initial volume (29.9 L)
T1 = initial temperature (33.0 °C + 273.15 = 306.15 K)
P2 = final pressure (385 mmHg)
T2 = final temperature (-16.2 °C + 273.15 = 256.95 K)
V2 = final volume (unknown)
Substituting the given values into the equation, we have:
(755 mmHg * 29.9 L) / (306.15 K) = (385 mmHg * V2) / (256.95 K)
Now we can solve for V2 by rearranging the equation:
V2 = (755 mmHg * 29.9 L * 256.95 K) / (385 mmHg * 306.15 K)
Canceling out units and simplifying, we get:
V2 = (755 * 29.9 * 256.95) / (385 * 306.15)
V2 ≈ 19.19 L
Therefore, the volume of the balloon at this altitude is approximately 19.19 L.