# Ideal gases

Tanya Sharma

## 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 .

Homework Helper

## 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

1 person
Tanya Sharma
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

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

Homework Helper

## 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

1 person
Homework Helper
Hi ehild

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

Tanya Sharma
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.

Homework Helper
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

1 person
Tanya Sharma
Thanks ehild and Andrew Mason