Guidance on finding the pressure and density of nitrogen

In summary, the question is asking to calculate the pressure and density of nitrogen at which the ideal gas equation of state has a 15% error for a plane flying in air at a temperature of 250 K. The equations provided are P = rho RT and Pv = RT. One approach to solving this problem is to substitute nitrogen with air, given that air is composed of about 78% nitrogen. However, the error due to this substitution should not have a significant impact. Any guidance on this problem would be appreciated.
  • #1
kawf
9
0

Homework Statement



Calculate the pressure and density of nitrogen at which there is a 15% error in the ideal gas equation of state for a plane flying in air of temperature 250 K

Homework Equations



P = rho RT
Pv = RT

The Attempt at a Solution



Little confused on how to approach the problem. Any guidance is appreciated.
 
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  • #2
i would suggest that since air is made up of about 78% nitrogen, you could substitute the nitrogen with air. anyway, there is already a 15% error in the equation. the error due to the substitution of nitrogen by air should not be very significant.

i might as well be wrong!
 
  • #3


I would suggest first reviewing the ideal gas equation of state and understanding its components (pressure, volume, temperature, and gas constant). From there, you can use the given information (temperature = 250 K and error = 15%) to set up an equation to solve for either pressure or density.

One approach could be to set the ideal gas equation of state equal to the 15% error value and solve for pressure or density. This would give you the pressure or density at which there is a 15% error in the equation.

Another approach could be to use the given equation Pv = RT to calculate the pressure at a specific volume (such as the volume of the plane) and then use that pressure to calculate the density using the equation P = rho RT.

In either case, it is important to carefully consider the units of measurement and ensure they are consistent in your calculations. Additionally, if you are unsure about any specific steps or calculations, consulting with a peer or mentor for guidance and clarification is always a good idea.
 

1. What is the formula for finding the pressure of nitrogen?

The formula for finding the pressure of nitrogen is P = nRT/V, where P is pressure, n is the number of moles of nitrogen, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume of the gas.

2. How do I determine the density of nitrogen?

The density of nitrogen can be determined by dividing the mass of the gas by its volume. The mass can be measured using a balance, and the volume can be calculated using the ideal gas law or by measuring the volume of the container holding the gas.

3. What units should I use for pressure and density when finding the values for nitrogen?

For pressure, the most commonly used unit is the Pascal (Pa), although other units such as atmospheres (atm) or millimeters of mercury (mmHg) may also be used. For density, the most commonly used unit is kilograms per cubic meter (kg/m3), although grams per liter (g/L) is also commonly used.

4. Is there a specific temperature that should be used when finding the pressure and density of nitrogen?

Yes, the temperature used should be in Kelvin (K) as the ideal gas law only works with absolute temperature. This means that the temperature in Celsius should be converted to Kelvin by adding 273.15 to the Celsius value.

5. Can the pressure and density of nitrogen change?

Yes, the pressure and density of nitrogen can change depending on the temperature and volume of the gas. According to the ideal gas law, as temperature increases, pressure and density also increase, while as volume increases, pressure and density decrease.

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