# Ideal gases

1. Oct 9, 2013

### Tanya Sharma

1. The problem statement, all variables and given/known data

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?

2. Relevant 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.

3. 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 .

2. Oct 9, 2013

### ehild

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. Oct 9, 2013

### Tanya Sharma

Hi ehild

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

4. Oct 9, 2013

### Andrew Mason

Correct.
Correct.
Correct, assuming you meant GM for that last GD.
Correct. Or you could say simply that the answer depends on how much less TD is than TM

AM

5. Oct 9, 2013

### ehild

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

ehild

6. Oct 10, 2013

### Tanya Sharma

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

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. Oct 10, 2013

### ehild

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. Oct 10, 2013

### Tanya Sharma

Thanks ehild and Andrew Mason