Ideal gases

  • #1
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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 .
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,911

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
 
  • #3
1,540
135
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
Andrew Mason
Science Advisor
Homework Helper
7,662
385

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
 
  • #5
ehild
Homework Helper
15,543
1,911
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
1,540
135
Correct, assuming you meant GM for that last GD

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

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
ehild
Homework Helper
15,543
1,911
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
 
  • #8
1,540
135
Thanks ehild and Andrew Mason
 

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