Entropy change in free expansion.

[ank160]

Suppose there are two parts in an insulated chamber, one filled with ideal gas and other is complete vaccum, separated by a partition. Now if partition is removed then gas will rush in other part to fill the whole chamber.

PROBLEM- Now there should be increase in entropy of system but i have read that there are only two ways through which entropy can increase-
1) by heat tranfer.
2) by the action of dissipiative forces which converts work into entropy.

But in above case niether of the case is applicable since there is no heat and work tranfer. So what is that which is causing increase in entropy of system. Please help.

 

[RedX]

Semantically you could argue that 2) is right.

When you remove the partition, one side of the gas is touching the vacuum. Therefore the rest of the gas will do work on that side of the gas, pushing it to fill the other chamber. Hence there is work being done. But eventually that side of the gas will fill the second chamber and halt when it slam into the walls of the chambers. When this happens dissipative forces will change the kinetic energy of the expanding gas into random thermal energy. This thermal energy will then heat up the other side of the gas which lost energy pushing the other side of the gas into the other chamber.

 

[ank160]

Semantically you could argue that 2) is right.

When you remove the partition, one side of the gas is touching the vacuum. Therefore the rest of the gas will do work on that side of the gas, pushing it to fill the other chamber. Hence there is work being done. But eventually that side of the gas will fill the second chamber and halt when it slam into the walls of the chambers. When this happens dissipative forces will change the kinetic energy of the expanding gas into random thermal energy. This thermal energy will then heat up the other side of the gas which lost energy pushing the other side of the gas into the other chamber.

here i want to mention two thigs-

a) does any dissipiative forces exist in case of ideal gases?
b) in case of ideal gas all collisions of gas molecules with wall will be elastic in nature so there won't be ne change in kinetic energy.

 

[Andrew Mason]

PROBLEM- Now there should be increase in entropy of system but i have read that there are only two ways through which entropy can increase-
1) by heat tranfer.
2) by the action of dissipiative forces which converts work into entropy.

What is your source for this?

Entropy changes because the reversible path between two states requires heat flow.

But in above case niether of the case is applicable since there is no heat and work tranfer. So what is that which is causing increase in entropy of system. Please help.

In this case there is no heat flow. But that does not determine whether there is a change in entropy. Entropy is a state function - it is the integral of dQ/T between the beginning and end states over the reversible path between those two states.

Here you have the case of a gas with initial thermodynamic state (P,V,T) = (P_0, V_0, T_0) and final state (P_0/2, 2V_0, T_0). The reversible path between these two states is an isothermal, quasi-static expansion. In such an expansion, work is done: $PdV \ne 0$. Since dU = 0 (constant T), an incremental expansion requires heat flow dQ = PdV. Over the entire expansion:

$$\Delta S = \int dQ/T = \int PdV/T = \int nRTdV/VT = nR\int dV/V = nR\ln(V_f/V_i)$$

AM

 

[ank160]

What is your source for this?

Entropy changes because the reversible path between two states requires heat flow.

In this case there is no heat flow. But that does not determine whether there is a change in entropy. Entropy is a state function - it is the integral of dQ/T between the beginning and end states over the reversible path between those two states.

Here you have the case of a gas with initial thermodynamic state (P,V,T) = (P_0, V_0, T_0) and final state (P_0/2, 2V_0, T_0). The reversible path between these two states is an isothermal, quasi-static expansion. In such an expansion, work is done: $PdV \ne 0$. Since dU = 0 (constant T), an incremental expansion requires heat flow dQ = PdV. Over the entire expansion:

$$\Delta S = \int dQ/T = \int PdV/T = \int nRTdV/VT = nR\int dV/V = nR\ln(V_f/V_i)$$

AM

Thanks 4 replyin but I am not convinced with ur explanation. Wot u have said is just a way of finding entropy change. But physically if u think then there must be some energy which is being convertde into entropy. i want to find out that sorce.

Guys please help!

 

[Andrew Mason]

Thanks 4 replyin but I am not convinced with ur explanation. Wot u have said is just a way of finding entropy change. But physically if u think then there must be some energy which is being convertde into entropy. i want to find out that sorce.

Guys please help!

If you haven't learned how to spell yet, you will have a great deal of difficulty learning about entropy.

What I have said is correct. So if you are not convinced, I would suggest that you read more about the subject. Entropy is a mathematical quantity. Energy is not converted into entropy. Total energy is always conserved. It is always there in some form. Entropy, on the other hand, always increases in real physical processes.

AM

 

[ank160]

If you haven't learned how to spell yet, you will have a great deal of difficulty learning about entropy.

What I have said is correct. So if you are not convinced, I would suggest that you read more about the subject. Entropy is a mathematical quantity. Energy is not converted into entropy. Total energy is always conserved. It is always there in some form. Entropy, on the other hand, always increases in real physical processes.

AM

Well Mr. Andrew Mason thanks 4 ur suggestion, I am surely going to study more abt entropy.

But i know how to spell entropy... its- E N T R O P Y , right? :)

another thing i want to mention that entropy is not a mathematical quantity , it is a THERMODYNAMIC quantity just like temperature.

Thanks!

 

[Andrew Mason]

another thing i want to mention that entropy is not a mathematical quantity , it is a THERMODYNAMIC quantity just like temperature.

The two are not mutually exclusive. Temperature is defined as a statistical concept - kinetic temperature - defined by the root-mean-square point of a Boltzmann distribution of molecular speeds. So it is definitely mathematical. But we also have a feel for temperature as a physical concept - it is how hot or cold something is. It is not so clear what the physical concept behind entropy is. If there is a non-mathematical way of explaining it perhaps you could let us know what it is.

AM

 

[ank160]

Energy is not converted into entropy. Total energy is always conserved. It is always there in some form. AM

The very basic defination of entropy says "its a dergree of randomness" and this the physical concept of entropy. Now if a system containing gas is provided with some external energy then its molecules will start moving rapidly and it will have greater randomness and thus higher entropy. Here external energy is getting converted into internal energy and also external energy causing entropy of system to increase. This way energy and entropy are connected to each other.

In literal sense yes energy can't be converted into entropy since they are two different entities nad have different dimensions.

 

[Andrew Mason]

The very basic defination of entropy says "its a dergree of randomness" and this the physical concept of entropy. Now if a system containing gas is provided with some external energy then its molecules will start moving rapidly and it will have greater randomness and thus higher entropy. Here external energy is getting converted into internal energy and also external energy causing entropy of system to increase. This way energy and entropy are connected to each other.

They are certainly connected. Entropy has dimensions of energy / temperature

In literal sense yes energy can't be converted into entropy since they are two different entities nad have different dimensions.

Mass can be converted into energy and vice-versa. They are two different entities with different dimensions.

AM