Question

A helium balloon contains 69.5 L of helium at sea level, where the atmosphere pressure is 101.3 kPa. The balloon is released frim a 4500 m mountaintop where the pressure is 61.7 kPa. What is the volume of the balloon when it takes off from the mountaintop

Answer 1

The new volume is 114.1 L

Step-by-step explanation:

Step 1: Data given

Volume of the helium balloon = 69.5 L

The atmosphere pressure is 101.3 kPa

The pressure decreases to 61.7 kPa

Step 2: Calculate the new volume

P1*V1 = P2*V2

⇒with P1 = the atmosphere pressure is 101.3 kPa

⇒with V1 = the initial volume = of the helium balloon = 69.5 L

⇒with P2 = the decreased pressure = 61.7 kPa

⇒with V2 = the new volume = TO BE DETERMINED

101.3 kPa * 69.5 L = 61.7 kPa * V2

V2 = (101.3 kPA * 69.5 L ) / 61.7 kPa

V2 = 114.1 L

The new volume is 114.1 L

Answer 2

THE NEW VOLUME WHEN THE BALLOON TAKES OFF FROM THE MOUNTAINTOP IS 114.1 L

Step-by-step explanation:

The question follows Boyle's law of gas laws and it involves pressure and volume being inversely proportional to the volume. As pressure increases, the volume decreases and vice versa.

Mathematically represented as:

P1V1 = P2 V2

P1 = 101.3 kPa = 101.3 * 10^3 Pa

V1 = 69.5 L

P2 = 61.7 kPa = 61.7 * 10^3 Pa

V2 = ?

making V2 the subject of the formula. we have;

V2 = P1 V1 / P2

V2 = 101.3 *10^3 * 69.5 / 61.7 *10^3

V2 = 7040.35 / 61.7

V2 = 114.106 L

The volume at a decreased pressure of 61.7 kPa at the mountaintop is 114.1 L

This is in line with Boyle's law which shows that at high pressure, volume decreases and at low pressure, volume increases.