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

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In a comparison of average translational kinetic energy and internal energy between diatomic gas (GD) and monoatomic gas (GM), it is established that at the same temperature, both gases have equal average translational kinetic energy. However, GD has a higher internal energy due to its greater degrees of freedom, quantified as (5/2)nRT for GD versus (3/2)nRT for GM. When the temperature of GM is higher than that of GD, GD's average translational kinetic energy is lower. The internal energy of GD can be greater than GM's if GD's temperature exceeds a specific threshold relative to GM's temperature. This highlights the complexity of energy relationships in ideal gases, particularly at varying temperatures.
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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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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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 .
 
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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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
 
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.
 
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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Thanks ehild and Andrew Mason
 

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