Comparing kinetic and internal energy of diatomic and monatomic ideal gases

[Tanya Sharma]

Homework Statement

Two closed containers A and B contain equal number of moles of ideal gases G_D (diatomic)and G_M (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 G_M ( T_M )is greater than G_D (T_D) ,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 G_D is (5/2)nRT is greater than internal energy of G_M ,which is (3/2)nRT


2.a) Since T_D < T_M ,the average translational kinetic energy of G_D is less than that of G_D.

2.b) When T_D < (3/5)T_M ,internal energy of G_D is less than that of G_M .But when (3/5)T_M <T_D <T_M ,the internal energy of G_D is more than that of G_M .

I would deeply appreciate if someone could check my work along with the reasoning .

 

[ehild]

Homework Statement

Two closed containers A and B contain equal number of moles of ideal gases G_D (diatomic)and G_M (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 G_M ( T_M )is greater than G_D (T_D) ,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 G_D is (5/2)nRT is greater than internal energy of G_M ,which is (3/2)nRT


2.a) Since T_D < T_M ,the average translational kinetic energy of G_D is less than that of G_D.

2.b) When T_D < (3/5)T_M ,internal energy of G_D is less than that of G_M .But when (3/5)T_M <T_D <T_M ,the internal energy of G_D is more than that of G_M .

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

ehild

 

[Tanya Sharma]

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

ehild

Hi ehild

Thanks for responding...In Q.2 it is given that T_D< T_M .

 

[Andrew Mason]

Homework Statement

Two closed containers A and B contain equal number of moles of ideal gases G_D (diatomic)and G_M (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 G_M ( T_M )is greater than G_D (T_D) ,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 G_D is (5/2)nRT is greater than internal energy of G_M ,which is (3/2)nRT

Correct.

2.a) Since T_D < T_M ,the average translational kinetic energy of G_D is less than that of G_D.

Correct, assuming you meant G_M for that last G_D.

2.b) When T_D < (3/5)T_M ,internal energy of G_D is less than that of G_M .But when (3/5)T_M <T_D <T_M ,the internal energy of G_D is more than that of G_M .

Correct. Or you could say simply that the answer depends on how much less T_D is than T_M

AM

 

[ehild]

Hi ehild

Thanks for responding...In Q.2 it is given that T_D< T_M .

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

ehild

 

[Tanya Sharma]

Correct, assuming you meant G_M for that last G_D

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.

 

[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.

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

 

[Tanya Sharma]

Thanks ehild and Andrew Mason