Ideal gas - monatomic or diatomic?

In summary, we have a problem where 5 moles of an ideal gas at 300K and 1.00 x 10^5 Pa is heated to 500K at constant pressure with 29.1 kJ of heat transferred. By considering the values of the molar heat capacity at constant pressure and constant volume, we can determine whether the gas is monatomic or diatomic. Using the equations PV = nRT, C = dQ/dT, Cp = Cv + nR, and Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas, we can calculate the ratio of Cp to nR and determine that for a monatomic gas it is
  • #1
shyguy79
102
0

Homework Statement



5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ.

Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure C sub c,m and at C sub v,m

Homework Equations


PV = nRT
C = dQ/dT
Cp = Cv + nR
Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas

The Attempt at a Solution


No idea where to start... help please!
 
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  • #2
shyguy79 said:

Homework Statement



5 moles of an idea gas at 300K at a pressure of 1.00 x 10^5 Pa is heated to 500K at constant pressure. The amount of heat transferred is 29.1kJ.

Determine whether a gas is monatomic or diatomic through consideration of the values of the molar heat capacity at constant pressure C sub c,m and at C sub v,m

Homework Equations


PV = nRT
C = dQ/dT
Cp = Cv + nR
Cv = f/2 nR where f = 3 for monatomic gas and f = 5 for diatomic gas

The Attempt at a Solution


No idea where to start... help please!

Hi shyguy79! :smile:

In a constant pressure process you have Cp=dQ/dT.
Can you calculate Cp from that?
What would you get if you divide Cp by nR?
 
  • #3
Where dQ = 29.1x10^3 and dT = 200K then Cp = 145.5 J K^-1

Is nR = 5 x 8.314 = 41.57 ? but why would you do this?

so Cp/nr = 3.5 ? How does this relate?
 
  • #4
Yep. That is correct.

What would Cp/nR be for a monatomic gas?
And for a diatomic gas?
 
  • #5
Cp = (f/2 +1) nR so then Cp/nR = (f/2 +1)

so for a monatomic gas... 3/2 + 1 = 2.5
for a diatomic gas... 5/2 +1 = 3.5

so the gas is diatomic?
 
  • #6
Right. :)
 
  • #7
Thank you so much! I've been stuck on this for ages!
 
  • #8
Just one question though what equation would be referenced for dividing Cp by nR?
 
  • #9
Not sure what you mean...?

You've used 3 of your relevant equations and solved for "f".
 
  • #10
doh! Yeah, just noticed - thanks again!
 

1. What is an ideal gas?

An ideal gas is a theoretical concept in physics and chemistry that describes the behavior of a gas at low pressures and high temperatures. It is a simplified model that assumes that gas particles have no volume and do not interact with each other, making their behavior predictable and easy to study.

2. What is the difference between a monatomic and diatomic ideal gas?

A monatomic ideal gas consists of single atoms as its constituent particles, while a diatomic ideal gas consists of molecules made up of two atoms bonded together, such as oxygen (O2) or nitrogen (N2). The main difference between the two is the number of particles in each gas molecule, which can affect their behavior and properties.

3. How do monatomic and diatomic ideal gases behave differently?

Monatomic ideal gases have simpler behavior compared to diatomic ideal gases. They have higher specific heat capacities and their internal energy depends only on temperature. On the other hand, diatomic ideal gases have lower specific heat capacities and their internal energy depends on both temperature and the number of particles in the gas molecule. Diatomic gases also have rotational and vibrational degrees of freedom, which can affect their behavior in certain conditions.

4. Can a real gas be considered as an ideal gas?

In most cases, no. Real gases have volume and can interact with each other, unlike ideal gases. However, at low pressures and high temperatures, some gases can behave closely to an ideal gas, making the ideal gas law a good approximation for their behavior. This is known as the ideal gas limit.

5. What is the significance of ideal gas behavior in scientific research?

Ideal gas behavior is important in many scientific fields, including chemistry, physics, and engineering. The ideal gas law is a fundamental equation that is used to calculate the behavior of gases in various conditions. It also serves as a starting point for more complex models that can describe the behavior of real gases. Additionally, the concept of ideal gases has led to important discoveries and advancements in our understanding of thermodynamics and the properties of matter.

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