Question

Karmina inflated a balloon at sea level, where the atmospheric pressure was 101. 3 kilopascals. The volume of the balloon was 2. 15 liters. She then carried the balloon with her to the top of a mountain, where the atmospheric pressure was 83. 1 kilopascals. If the temperature was constant and no air leaked out of the balloon, what was the balloon’s volume at the top of the mountain?

Answer 1

2.62 L

Step-by-step explanation:

This problem can be solved using the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature in kelvins.

In this case, we can assume that the number of moles of gas and the temperature are constant, since the balloon is not leaking and the temperature is not changing. Therefore, we can write:

P1V1 = P2V2

where P1 and V1 are the pressure and volume at sea level, and P2 and V2 are the pressure and volume at the top of the mountain.

Substituting the given values, we get:

(101.3 kPa)(2.15 L) = (83.1 kPa)(V2)

Solving for V2, we get:

V2 = (101.3 kPa)(2.15 L) / (83.1 kPa) ≈ 2.62 L

Therefore, the balloon's volume at the top of the mountain is approximately 2.62 liters.