Question

A spherical balloon is made from a material whose mass is 4.30 kg. The thickness of the material is negligible compared to the 1.54-m radius of the balloon. The balloon is filled with helium (He) at a temperature of 289 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m3. Find the absolute pressure of the helium gas.

Answer 1

The absolute pressure of the helium gas inside the balloon is 1.19 atmospheres.

Step-by-step explanation:

The absolute pressure of the helium gas inside the balloon can be calculated using the ideal gas law equation, which states that:

PV = nRT

Where:

• P is the pressure
• V is the volume
• n is the number of moles
• R is the ideal gas constant
• T is the temperature in Kelvin

In this case, since the balloon is floating in the air without rising or falling, the pressure inside the balloon is equal to the pressure outside the balloon (atmospheric pressure).

Using the given information, we can calculate the number of moles of helium in the balloon by dividing the mass of the helium by its molar mass. Then, we can substitute the known values into the ideal gas law equation to find the absolute pressure of the helium gas.

The absolute pressure of the helium gas inside the balloon is 1.19 atmospheres.

Answer 2

P = 5.97 × 10^(5) Pa

Step-by-step explanation:

We are given;

Mass of balloon;m_b = 4.3 kg

Radius;r = 1.54 m

Temperature;T = 289 K

Density;ρ = 1.19 kg/m³

We know that, density = mass/volume

So, mass = Volume x Density

We also know that Force = mg

Thus;

F = mg = Vρg

Where m = mass of balloon(m_b) + mass of helium (m_he)

So,

(m_b + m_he)g = Vρg

g will cancel out to give;

(m_b + m_he) = Vρ - - - eq1

Since a sphere shaped balloon, Volume(V) = (4/3)πr³

V = (4/3)π(1.54)³

V = 15.3 m³

Plugging relevant values into equation 1,we have;

(3 + m_he) = 15.3 × 1.19

m_he = 18.207 - 3

m_he = 15.207 kg = 15207 g

Molecular weight of helium gas is 4 g/mol

Thus, Number of moles of helium gas is ; no. of moles = 15207/4 ≈ 3802 moles

From ideal gas equation, we know that;

P = nRT/V

Where,

P is absolute pressure

n is number of moles

R is the gas constant and has a value lf 8.314 J/mol.k

T is temperature

V is volume

Plugging in the relevant values, we have;

P = (3802 × 8.314 × 289)/15.3

P = 597074.53 Pa

P = 5.97 × 10^(5) Pa