Comparing Average Translational Kinetic Energy and Internal Energy of GD and GM

In summary: I deeply appreciate it...Have a nice day ahead!! In summary, the conversation discusses two closed containers, A and B, containing equal number of moles of ideal gases GD (diatomic) and GM (monoatomic), respectively. The questions revolve around the average translational kinetic energy and internal energy of these gases, with a focus on the temperature of each gas. It is determined that at equal temperatures, the average translational kinetic energy is the same for both gases. However, the internal energy of GD is greater than that of GM. When the temperature of GM is greater than that of GD, the average translational kinetic energy of GD is less than that of GM. The internal energy of GD is also
  • #1
Tanya Sharma
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Homework Statement



Two closed containers A and B contain equal number of moles of ideal gases GD (diatomic)and GM (Monoatomic) ,respectively.

Q .1 a) If the temperature of gases are same,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy ?

Q.2 a) If the temperature of GM ( TM )is greater than GD (TD) ,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy?



Homework Equations



Average translational kinetic energy of n moles of ideal gas= (3/2)nRT

Internal energy of n moles of ideal gas =(f/2)nRT ,f is the degree of freedom.


The Attempt at a Solution



1.a) Since the temperature is equal,average translational kinetic energy of both the gases is same .

1.b) The internal energy of GD is (5/2)nRT is greater than internal energy of GM ,which is (3/2)nRT


2.a) Since TD < TM ,the average translational kinetic energy of GD is less than that of GD.

2.b) When TD < (3/5)TM ,internal energy of GD is less than that of GM .But when (3/5)TM <TD <TM ,the internal energy of GD is more than that of GM .

I would deeply appreciate if someone could check my work along with the reasoning .
 
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  • #2
Tanya Sharma said:

Homework Statement



Two closed containers A and B contain equal number of moles of ideal gases GD (diatomic)and GM (Monoatomic) ,respectively.

Q .1 a) If the temperature of gases are same,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy ?

Q.2 a) If the temperature of GM ( TM )is greater than GD (TD) ,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy?



Homework Equations



Average translational kinetic energy of n moles of ideal gas= (3/2)nRT

Internal energy of n moles of ideal gas =(f/2)nRT ,f is the degree of freedom.


The Attempt at a Solution



1.a) Since the temperature is equal,average translational kinetic energy of both the gases is same .

1.b) The internal energy of GD is (5/2)nRT is greater than internal energy of GM ,which is (3/2)nRT


2.a) Since TD < TM ,the average translational kinetic energy of GD is less than that of GD.

2.b) When TD < (3/5)TM ,internal energy of GD is less than that of GM .But when (3/5)TM <TD <TM ,the internal energy of GD is more than that of GM .

It is correct, but is the internal energy of the diatomic gas not greater than that of the monoatomic gas for all TD> (3/5)TM?

ehild
 
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  • #3
ehild said:
It is correct, but is the internal energy of the diatomic gas not greater than that of the monoatomic gas for all TD> (3/5)TM?

ehild

Hi ehild :smile:

Thanks for responding...In Q.2 it is given that TD< TM .
 
  • #4
Tanya Sharma said:

Homework Statement



Two closed containers A and B contain equal number of moles of ideal gases GD (diatomic)and GM (Monoatomic) ,respectively.

Q .1 a) If the temperature of gases are same,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy ?

Q.2 a) If the temperature of GM ( TM )is greater than GD (TD) ,which of them has more average translational kinetic energy ?

b) Which of them has more internal energy?



Homework Equations



Average translational kinetic energy of n moles of ideal gas= (3/2)nRT

Internal energy of n moles of ideal gas =(f/2)nRT ,f is the degree of freedom.


The Attempt at a Solution



1.a) Since the temperature is equal,average translational kinetic energy of both the gases is same .
Correct.
1.b) The internal energy of GD is (5/2)nRT is greater than internal energy of GM ,which is (3/2)nRT
Correct.
2.a) Since TD < TM ,the average translational kinetic energy of GD is less than that of GD.
Correct, assuming you meant GM for that last GD.
2.b) When TD < (3/5)TM ,internal energy of GD is less than that of GM .But when (3/5)TM <TD <TM ,the internal energy of GD is more than that of GM .
Correct. Or you could say simply that the answer depends on how much less TD is than TM

AM
 
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  • #5
Tanya Sharma said:
Hi ehild :smile:

Thanks for responding...In Q.2 it is given that TD< TM .

I see. Still, I see it confusing. It is not needed anyway.

ehild
 
  • #6
Andrew Mason said:
Correct, assuming you meant GM for that last GD

Thanks Andrew...Yes that was typo...

ehild said:
I see. Still, I see it confusing. It is not needed anyway.

ehild

Okay...

The answer to Q2.b) is a bit surprising to me .Even though the temperature of diatomic gas is less than that of the monoatomic gas ,its internal energy is more than that of latter.
 
  • #7
Tanya Sharma said:
Okay...

The answer to Q2.b) is a bit surprising to me .Even though the temperature of diatomic gas is less than that of the monoatomic gas ,its internal energy is more than that of latter.

It can be more than that of the monoatomic molecule.

There is 1/2 kT energy for each degrees in average, so a diatomic molecule has more energy than the monoatomic one in average as it can also rotate, at medium temperatures. At very high temperatures, even the vibration of the diatomic molecule would be excited, and it would posses even higher energy, 7/2 kT.

ehild
 
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  • #8
Thanks ehild and Andrew Mason
 

FAQ: Comparing Average Translational Kinetic Energy and Internal Energy of GD and GM

What is the difference between average translational kinetic energy and internal energy?

Average translational kinetic energy is the measure of the average speed of particles in a system, while internal energy is the total energy of all the particles in a system, including both kinetic and potential energy.

How are average translational kinetic energy and internal energy related in a system?

The average translational kinetic energy of a system is a component of the total internal energy. Other factors that contribute to internal energy include the potential energy of particles and the energy associated with intermolecular forces.

How do the average translational kinetic energy and internal energy compare in gases and liquids?

In gases, the average translational kinetic energy is the dominant contributor to the internal energy. In liquids, however, the average translational kinetic energy is smaller compared to the potential energy of particles and intermolecular forces.

How do the average translational kinetic energy and internal energy change with temperature?

As temperature increases, so does the average translational kinetic energy of particles. However, the internal energy may not change at the same rate, as potential energy and intermolecular forces can also contribute to internal energy.

In which type of system would the difference between average translational kinetic energy and internal energy be most significant?

The difference between average translational kinetic energy and internal energy would be most significant in a solid system, as the particles are more closely packed and have less translational motion, resulting in a larger contribution of potential energy and intermolecular forces to the internal energy.

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