Question

For some reason, a skier decides to ski from the summit of a mountain near Park City, UT (elevation = 9970 ft, T= -18.0 °C, and Patm = 623 mm Hg), to the base of the mountain (elevation = 6920 feet, T = -13 °C, and Patm = 688 mm Hg) with a balloon tied to each of her ski poles. If each balloon is filled to a volume of 1.80 L at the summit, what is the volume of each balloon at the base?

Answer 1

The volume of each balloon at the base is approximately 2.06 L.

Step-by-step explanation:

To find the volume of each balloon at the base, we need to use the combined gas law, which states that the product of the initial pressure, volume, and temperature is equal to the product of the final pressure, volume, and temperature.

Using the information provided:

P1 = 623 mm Hg, V1 = 1.80 L, T1 = -18.0 °C

P2 = 688 mm Hg, V2 = ?, T2 = -13.0 °C

We can solve for V2:

P1 * V1 * T2 = P2 * V2 * T1

Plugging in the values, we get:

(623 mm Hg) * (1.80 L) * (-13.0 °C) = (688 mm Hg) * V2 * (-18.0 °C)

Simplifying the equation, we find that the volume of each balloon at the base is approximately 2.06 L.