Is the Gas in the Tank Helium or Oxygen?

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Homework Statement

A 2-ft$$^{3}$$ closed tank is filled with 0.30 lb (Weight) of gas, which is thought to be either oxygen or helium. A pressure gage attached to the tank reads 12 psi at a temperature of T=80F. Is it He or O$$_{2}$$? Why? Jeopardizing safety?

Homework Equations

$$\gamma$$=weight/volume

$$\gamma$$=$$\rho$$*g

where $$\rho$$ is the specific density.

$$\rho$$=p/RT

where p is pressure, R is engineering gas constant, and T is temperature in Rankine.

The Attempt at a Solution

In this case, I'm looking for R. I know R$$_{oxygen}$$=1554 ft-lb/slug*Rankine and R$$_{helium}$$=12419 ft-lb/slug*Rankine.

So I know $$\gamma$$, which is 0.30-lb/2-ft$$^{3}$$=0.15-lb/ft$$^{3}$$

so, since $$\gamma$$=$$\rho$$*g=Pg/RT

and T(R) = 539.6 Rankine

R=Pg/$$\gamma$$T=((32.2 ft/s$$^{2}$$)*(12psi*144 lbs/ft$$^{2}$$/psi))/((0.15-lb/ft$$^{3}$$)*539.6 Rankine)

R=477.391 ft$$^{2}$$/(s$$^{2}$$*Rankine)

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I'm not sure where I'm going wrong with this, but it should either be 1554 or 12419... Oh, and my units are off too.

 

[CFDFEAGURU]

Yes, your units are way off. However, the answer lies inside the units. One unit for the gas constant is;

(psia*ft^3)/(lbm*R)

Compare these units to the ones stated in your problem and try for the solution again using the ideal gas equation.

Also, you don't need to convert 0.30 lbs to slugs.

Thanks
Matt

 

[tomcue]

Firstly, I would like to clarify that the given information is not enough to determine whether the gas in the tank is helium or oxygen. This is because both gases have different molecular weights and can have the same pressure and temperature at the same time.

To solve this pressure problem, we need to use the ideal gas law, which states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Since we are given the pressure (12 psi), volume (2 ft^3), and temperature (80F), we can rearrange the equation to solve for n, the number of moles.

n = (PV)/(RT)

To calculate the number of moles, we need to know the gas constant, R. As you correctly stated, the gas constant for oxygen is 1554 ft-lb/slug*Rankine and for helium is 12419 ft-lb/slug*Rankine. However, we also need to consider the units of pressure and volume. The given pressure is in psi, and the given volume is in ft^3. Therefore, we need to convert the pressure to lb/ft^2 and the volume to in^3.

12 psi = (12 lb/in^2)(144 in^2/ft^2) = 1728 lb/ft^2

2 ft^3 = (2 ft^3)(12 in/ft)^3 = 3456 in^3

Substituting these values into the equation, we get:

n = ((1728 lb/ft^2)(3456 in^3))/(477.391 ft^2/s^2*Rankine)(80F + 459.67)

= 0.0081 moles

Now, to determine whether the gas is helium or oxygen, we need to calculate the specific density, \gamma, which is the weight of the gas divided by its volume. We know the weight of the gas is 0.30 lb, and the volume is 2 ft^3. Therefore,

\gamma = (0.30 lb)/(2 ft^3) = 0.15 lb/ft^3

Next, we need to calculate the specific density using the ideal gas law:

\rho = (P/RT)

Substituting the values for pressure, temperature, and R (for helium and oxygen), we get