Moles of gas helium balloon; buoyancy; PV=nRT

In summary, the question asks for the number of moles of helium gas contained in a balloon, which is used to lift a load of 101N. The weight of the envelope of the balloon is 46.5N and the volume of the helium when the balloon is fully inflated is 31.5m3. The temperature of the air is 0°C and the atmospheric pressure is 1.00 atm. The net upward force on the balloon and its load is 32.1N. To find the number of moles, the Archimedes Principle is used to calculate the mass of helium required, and then the moles can be calculated using the ideal gas law. The suggested method of calculating the mass using the
  • #1
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Homework Statement


A helium balloon is used to lift a load of101N. The weight of the envelope of the balloon is46.5N and the volume of the helium when the balloon is fully inflated is31.5m3. The temperature of the air is 0°C and the atmospheric pressure is 1.00 atm. The balloon is inflated with a sufficient amount of helium gas that the net upward force on the balloon and its load is32.1N. Neglect any effects due to the changes of temperature as the altitude changes.

a) How many moles of helium gas are contained in the balloon?

b) At what altitude will the balloon be fully inflated?

(I'm still stuck on part a)

Homework Equations


PV = nRT; n = PV/RT

V = m/d

The Attempt at a Solution


If we solve PV=nRT for the number of moles, that should give us the number of moles of helium.

We are given the pressure of 1 atm, temperature of 0 C, and R is constant. We are not given the volume.

Converted to consistent units, we have:

P = 101325 Pa

T = 273.15 K

R = 8.314 J/mol*k

V = ? m^3

So, we need to find the volume.

V = m/d

We can look up the density of helium, but the mass is not directly given.

d = 0.179(kg/m^3)

We can calculate the mass by using the net force. The Archimedes Principle says that the net upward force (buoyant force)is equal to the weight of fluid displaced. The fluid displaced is equal to the fluid of helium inside the balloon.

The net upward force is 32.1 N

F = ma

m = F/a

m = 32.1N / 9.8(m/s^2) = 3.276 kg

V = m/d = 3.276kg / 0.179(kg/m^3) = 18.299 m^3

V = 18.299 m^3

So, now we have P, T, R, and V

n = PV/RT

n = (101325 Pa)( 18.299 m^3) / [ (8.314 J/mol*k)(273.15 k) ]

n = 816.45 mol

So, I get 816 mol, and the answer given for the problem is 734 mol.

I feel like I've checked pretty carefully to make sure units are in agreement and that I'm using the right values for constants. I also feel like the approach is correct, especially since the hint after submitting my answer said to use the Archimedes Principle to find the volume. I've been working on this problem for an embarrassingly long time, so I'd appreciate fresh eyes on it.

For reference, this problem is in the thermodynamics portion of physics 3.
 
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  • #2
rsera said:

Homework Statement


A helium balloon is used to lift a load of101N. The weight of the envelope of the balloon is46.5N and the volume of the helium when the balloon is fully inflated is31.5m3. The temperature of the air is 0°C and the atmospheric pressure is 1.00 atm. The balloon is inflated with a sufficient amount of helium gas that the net upward force on the balloon and its load is32.1N. Neglect any effects due to the changes of temperature as the altitude changes.

a) How many moles of helium gas are contained in the balloon?

b) At what altitude will the balloon be fully inflated?

(I'm still stuck on part a)

Homework Equations


PV = nRT; n = PV/RT

V = m/d

The Attempt at a Solution


If we solve PV=nRT for the number of moles, that should give us the number of moles of helium.

We are given the pressure of 1 atm, temperature of 0 C, and R is constant. We are not given the volume.

Converted to consistent units, we have:

P = 101325 Pa

T = 273.15 K

R = 8.314 J/mol*k

V = ? m^3

So, we need to find the volume.

V = m/d

We can look up the density of helium, but the mass is not directly given.

d = 0.179(kg/m^3)

We can calculate the mass by using the net force. The Archimedes Principle says that the net upward force (buoyant force)is equal to the weight of fluid displaced. The fluid displaced is equal to the fluid of helium inside the balloon.

No, it is wrong.What is the fluid the balloon is in? What is the "displaced fluid"? Displaced from the volume of the balloon...
 
  • #3
The basic principle is:
The displaced air should exert a net upwards force that is greater than the total downward force.

By this, calculate the mass of helium required. Moles can be easily calculated once you get the mass.
 

1. What is the relationship between the number of moles of gas and the volume of a helium balloon?

The number of moles of gas and the volume of a helium balloon have a direct relationship, meaning that as the number of moles increases, so does the volume. This is due to the ideal gas law, which states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles present.

2. How does buoyancy affect a helium balloon?

Buoyancy is the upward force exerted on an object immersed in a fluid. In the case of a helium balloon, the gas inside is less dense than the surrounding air, causing it to rise due to the buoyant force. This is why helium balloons float in the air.

3. What is the significance of the ideal gas law in relation to a helium balloon?

The ideal gas law, represented by the equation PV=nRT, is used to describe the behavior of gases under various conditions. In the case of a helium balloon, this law helps us understand the relationship between the volume of the balloon, the number of moles of gas, and the temperature and pressure of the surrounding air.

4. How does temperature affect the volume of a helium balloon?

According to the ideal gas law, as temperature increases, the volume of a gas also increases. This means that a helium balloon will expand and become larger as the surrounding air temperature increases. On the other hand, if the temperature decreases, the volume of the balloon will also decrease.

5. What is the significance of the number of moles of gas in a helium balloon?

The number of moles of gas in a helium balloon determines its volume and ultimately its buoyancy. More moles of gas will result in a larger volume and a greater buoyant force, causing the balloon to rise higher. The number of moles also affects the pressure inside the balloon, as described by the ideal gas law.

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