Equalization of pressure in heat exchanger
Clash Royale CLAN TAG#URR8PPP
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I was solving numericals on Kinetic Theory of Gases when I came across this question
Two closed vessel of equal volume contain air at 105 kPa, 300K and are connected through narrow tube. If one of the vessel is now maintained at 300K and other at 400K what will be the pressure in the vessel?
I don't want the solution of this question but I want to know why the pressure will be same in both the vessel when one is maintained 300K and other 400K. The molecules in the vessel at 400K will have greater kinetic energy and will exert greater pressure on the walls than the molecules of the other vessel.
Now one will say that some of the molecules of vessel at higher temperature will move to the other vessel so that the pressure remains same in both the vessels, but why is it so. Why can't the pressure in both the vessels be different?
pressure kinetic-theory-of-gases
add a comment |Â
up vote
3
down vote
favorite
I was solving numericals on Kinetic Theory of Gases when I came across this question
Two closed vessel of equal volume contain air at 105 kPa, 300K and are connected through narrow tube. If one of the vessel is now maintained at 300K and other at 400K what will be the pressure in the vessel?
I don't want the solution of this question but I want to know why the pressure will be same in both the vessel when one is maintained 300K and other 400K. The molecules in the vessel at 400K will have greater kinetic energy and will exert greater pressure on the walls than the molecules of the other vessel.
Now one will say that some of the molecules of vessel at higher temperature will move to the other vessel so that the pressure remains same in both the vessels, but why is it so. Why can't the pressure in both the vessels be different?
pressure kinetic-theory-of-gases
1
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
1
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I was solving numericals on Kinetic Theory of Gases when I came across this question
Two closed vessel of equal volume contain air at 105 kPa, 300K and are connected through narrow tube. If one of the vessel is now maintained at 300K and other at 400K what will be the pressure in the vessel?
I don't want the solution of this question but I want to know why the pressure will be same in both the vessel when one is maintained 300K and other 400K. The molecules in the vessel at 400K will have greater kinetic energy and will exert greater pressure on the walls than the molecules of the other vessel.
Now one will say that some of the molecules of vessel at higher temperature will move to the other vessel so that the pressure remains same in both the vessels, but why is it so. Why can't the pressure in both the vessels be different?
pressure kinetic-theory-of-gases
I was solving numericals on Kinetic Theory of Gases when I came across this question
Two closed vessel of equal volume contain air at 105 kPa, 300K and are connected through narrow tube. If one of the vessel is now maintained at 300K and other at 400K what will be the pressure in the vessel?
I don't want the solution of this question but I want to know why the pressure will be same in both the vessel when one is maintained 300K and other 400K. The molecules in the vessel at 400K will have greater kinetic energy and will exert greater pressure on the walls than the molecules of the other vessel.
Now one will say that some of the molecules of vessel at higher temperature will move to the other vessel so that the pressure remains same in both the vessels, but why is it so. Why can't the pressure in both the vessels be different?
pressure kinetic-theory-of-gases
pressure kinetic-theory-of-gases
edited 18 mins ago
Mithoron
3,59882744
3,59882744
asked 4 hours ago
Loop Back
33519
33519
1
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
1
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago
add a comment |Â
1
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
1
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago
1
1
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
1
1
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago
add a comment |Â
3 Answers
3
active
oldest
votes
up vote
3
down vote
accepted
Macroscopics
Imagine the tube is initially closed. Then one vessel is heated up. As $V$ and $m$ are constant:
$$P=k,T$$
So if T is increased, P is increased. As $P$ is increased, there will be a net flow of mass, until they are balanced. That's what we observe. Now, we can think of it microscopically.
Microscopics
Initially, there are the same number of particles in each vessel. When heating up there is an increase in velocity. So, in the high temperature vessel the same number of molecules are with higher velocity. Imagine a plane in the middle of the narrow tube, the number of collisions per unit time, because of velocity, will be higher in 400$rightarrow$300 direction...it indicates a net flow of mass. This flow of mass will equal pressures on both sides.
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
 |Â
show 1 more comment
up vote
1
down vote
This experiment divides the container so that pressure (a "flow" of gas molecules against the walls) can be equalized thru the narrow tube but net flow of heat from hot molecules passing thru the narrow tube is seriously impeded (essentially does not occur because each section is maintained at 300K or 400K).
This non-equilibrium condition is held static by the external devices maintaining the set temperatures and the narrow tube which connects the pressures in the two "systems" but disconnects the heat flow.
To see that the pressures will eventually be the same, imagine connecting the two vessels at 300K by the narrow tube, then quickly heating one to 400K. The pressure will increase in the heated tube, and depending on the narrowness of the tube, will decrease as gas flows into the cooler tube (where the pressure will increase because there will be more molecules there, even tho still at 300K). After some time, the pressures will equalize.
add a comment |Â
up vote
1
down vote
To answer your question directly: Why can't the pressure in both the vessels be different? The answer is that the system is closed, and the number of molecules is conserved - molecules cannot enter from outside the two vessels. Thus, molecules can't move from the hotter vessel to the cooler vessel forever - the hotter vessel would run out of molecules.
The critical part of the ideal gas law to keep in mind is the $N$ - the number of molecules: $$PV = Nk_BT.$$ In the hotter vessel, molecules will travel out, and $N$ will be reduced, as long as the pressure is greater than the cooler vessel. Since volume and temperature are constant, pressure must drop until the pressures are equal.
New contributor
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
add a comment |Â
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Macroscopics
Imagine the tube is initially closed. Then one vessel is heated up. As $V$ and $m$ are constant:
$$P=k,T$$
So if T is increased, P is increased. As $P$ is increased, there will be a net flow of mass, until they are balanced. That's what we observe. Now, we can think of it microscopically.
Microscopics
Initially, there are the same number of particles in each vessel. When heating up there is an increase in velocity. So, in the high temperature vessel the same number of molecules are with higher velocity. Imagine a plane in the middle of the narrow tube, the number of collisions per unit time, because of velocity, will be higher in 400$rightarrow$300 direction...it indicates a net flow of mass. This flow of mass will equal pressures on both sides.
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
 |Â
show 1 more comment
up vote
3
down vote
accepted
Macroscopics
Imagine the tube is initially closed. Then one vessel is heated up. As $V$ and $m$ are constant:
$$P=k,T$$
So if T is increased, P is increased. As $P$ is increased, there will be a net flow of mass, until they are balanced. That's what we observe. Now, we can think of it microscopically.
Microscopics
Initially, there are the same number of particles in each vessel. When heating up there is an increase in velocity. So, in the high temperature vessel the same number of molecules are with higher velocity. Imagine a plane in the middle of the narrow tube, the number of collisions per unit time, because of velocity, will be higher in 400$rightarrow$300 direction...it indicates a net flow of mass. This flow of mass will equal pressures on both sides.
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
 |Â
show 1 more comment
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Macroscopics
Imagine the tube is initially closed. Then one vessel is heated up. As $V$ and $m$ are constant:
$$P=k,T$$
So if T is increased, P is increased. As $P$ is increased, there will be a net flow of mass, until they are balanced. That's what we observe. Now, we can think of it microscopically.
Microscopics
Initially, there are the same number of particles in each vessel. When heating up there is an increase in velocity. So, in the high temperature vessel the same number of molecules are with higher velocity. Imagine a plane in the middle of the narrow tube, the number of collisions per unit time, because of velocity, will be higher in 400$rightarrow$300 direction...it indicates a net flow of mass. This flow of mass will equal pressures on both sides.
Macroscopics
Imagine the tube is initially closed. Then one vessel is heated up. As $V$ and $m$ are constant:
$$P=k,T$$
So if T is increased, P is increased. As $P$ is increased, there will be a net flow of mass, until they are balanced. That's what we observe. Now, we can think of it microscopically.
Microscopics
Initially, there are the same number of particles in each vessel. When heating up there is an increase in velocity. So, in the high temperature vessel the same number of molecules are with higher velocity. Imagine a plane in the middle of the narrow tube, the number of collisions per unit time, because of velocity, will be higher in 400$rightarrow$300 direction...it indicates a net flow of mass. This flow of mass will equal pressures on both sides.
edited 3 hours ago
answered 3 hours ago
santimirandarp
1,245222
1,245222
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
 |Â
show 1 more comment
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
I can't follow, so what if the collision rate is greater in the vessel at higher temperature? I want to know why will the pressure will be same in both the vessels
â Loop Back
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
Hi..! If the collision rate is higher, pressure is higher...@LoopBack
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
If we imagine a plane in the middle of the tubes, as the collision rate is higher, there is a net flow of mass, so the pressure on the lower temperature side will be increased @LoopBack. Isn't what you're asking?
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
@LoopBack the question is clear, there is a net flow of mass because collision rate is higher in the high temperature vessel. This flow of mass rises up the pressure on the low temperature side. That's all...
â santimirandarp
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
thank you. Answer is clear as well.
â Loop Back
3 hours ago
 |Â
show 1 more comment
up vote
1
down vote
This experiment divides the container so that pressure (a "flow" of gas molecules against the walls) can be equalized thru the narrow tube but net flow of heat from hot molecules passing thru the narrow tube is seriously impeded (essentially does not occur because each section is maintained at 300K or 400K).
This non-equilibrium condition is held static by the external devices maintaining the set temperatures and the narrow tube which connects the pressures in the two "systems" but disconnects the heat flow.
To see that the pressures will eventually be the same, imagine connecting the two vessels at 300K by the narrow tube, then quickly heating one to 400K. The pressure will increase in the heated tube, and depending on the narrowness of the tube, will decrease as gas flows into the cooler tube (where the pressure will increase because there will be more molecules there, even tho still at 300K). After some time, the pressures will equalize.
add a comment |Â
up vote
1
down vote
This experiment divides the container so that pressure (a "flow" of gas molecules against the walls) can be equalized thru the narrow tube but net flow of heat from hot molecules passing thru the narrow tube is seriously impeded (essentially does not occur because each section is maintained at 300K or 400K).
This non-equilibrium condition is held static by the external devices maintaining the set temperatures and the narrow tube which connects the pressures in the two "systems" but disconnects the heat flow.
To see that the pressures will eventually be the same, imagine connecting the two vessels at 300K by the narrow tube, then quickly heating one to 400K. The pressure will increase in the heated tube, and depending on the narrowness of the tube, will decrease as gas flows into the cooler tube (where the pressure will increase because there will be more molecules there, even tho still at 300K). After some time, the pressures will equalize.
add a comment |Â
up vote
1
down vote
up vote
1
down vote
This experiment divides the container so that pressure (a "flow" of gas molecules against the walls) can be equalized thru the narrow tube but net flow of heat from hot molecules passing thru the narrow tube is seriously impeded (essentially does not occur because each section is maintained at 300K or 400K).
This non-equilibrium condition is held static by the external devices maintaining the set temperatures and the narrow tube which connects the pressures in the two "systems" but disconnects the heat flow.
To see that the pressures will eventually be the same, imagine connecting the two vessels at 300K by the narrow tube, then quickly heating one to 400K. The pressure will increase in the heated tube, and depending on the narrowness of the tube, will decrease as gas flows into the cooler tube (where the pressure will increase because there will be more molecules there, even tho still at 300K). After some time, the pressures will equalize.
This experiment divides the container so that pressure (a "flow" of gas molecules against the walls) can be equalized thru the narrow tube but net flow of heat from hot molecules passing thru the narrow tube is seriously impeded (essentially does not occur because each section is maintained at 300K or 400K).
This non-equilibrium condition is held static by the external devices maintaining the set temperatures and the narrow tube which connects the pressures in the two "systems" but disconnects the heat flow.
To see that the pressures will eventually be the same, imagine connecting the two vessels at 300K by the narrow tube, then quickly heating one to 400K. The pressure will increase in the heated tube, and depending on the narrowness of the tube, will decrease as gas flows into the cooler tube (where the pressure will increase because there will be more molecules there, even tho still at 300K). After some time, the pressures will equalize.
answered 3 hours ago
James Gaidis
1,78329
1,78329
add a comment |Â
add a comment |Â
up vote
1
down vote
To answer your question directly: Why can't the pressure in both the vessels be different? The answer is that the system is closed, and the number of molecules is conserved - molecules cannot enter from outside the two vessels. Thus, molecules can't move from the hotter vessel to the cooler vessel forever - the hotter vessel would run out of molecules.
The critical part of the ideal gas law to keep in mind is the $N$ - the number of molecules: $$PV = Nk_BT.$$ In the hotter vessel, molecules will travel out, and $N$ will be reduced, as long as the pressure is greater than the cooler vessel. Since volume and temperature are constant, pressure must drop until the pressures are equal.
New contributor
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
add a comment |Â
up vote
1
down vote
To answer your question directly: Why can't the pressure in both the vessels be different? The answer is that the system is closed, and the number of molecules is conserved - molecules cannot enter from outside the two vessels. Thus, molecules can't move from the hotter vessel to the cooler vessel forever - the hotter vessel would run out of molecules.
The critical part of the ideal gas law to keep in mind is the $N$ - the number of molecules: $$PV = Nk_BT.$$ In the hotter vessel, molecules will travel out, and $N$ will be reduced, as long as the pressure is greater than the cooler vessel. Since volume and temperature are constant, pressure must drop until the pressures are equal.
New contributor
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
add a comment |Â
up vote
1
down vote
up vote
1
down vote
To answer your question directly: Why can't the pressure in both the vessels be different? The answer is that the system is closed, and the number of molecules is conserved - molecules cannot enter from outside the two vessels. Thus, molecules can't move from the hotter vessel to the cooler vessel forever - the hotter vessel would run out of molecules.
The critical part of the ideal gas law to keep in mind is the $N$ - the number of molecules: $$PV = Nk_BT.$$ In the hotter vessel, molecules will travel out, and $N$ will be reduced, as long as the pressure is greater than the cooler vessel. Since volume and temperature are constant, pressure must drop until the pressures are equal.
New contributor
To answer your question directly: Why can't the pressure in both the vessels be different? The answer is that the system is closed, and the number of molecules is conserved - molecules cannot enter from outside the two vessels. Thus, molecules can't move from the hotter vessel to the cooler vessel forever - the hotter vessel would run out of molecules.
The critical part of the ideal gas law to keep in mind is the $N$ - the number of molecules: $$PV = Nk_BT.$$ In the hotter vessel, molecules will travel out, and $N$ will be reduced, as long as the pressure is greater than the cooler vessel. Since volume and temperature are constant, pressure must drop until the pressures are equal.
New contributor
New contributor
answered 1 hour ago
T.C. Proctor
1111
1111
New contributor
New contributor
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
add a comment |Â
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
Nice answer, any chance you want to add discussion on chemical potential to more complete? (So I don't have to)
â A.K.
1 hour ago
add a comment |Â
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1
The pressure can't be different precisely because the vessels are connected, and some molecules will move to the other vessel to equalize it. That's what pressure is all about.
â Ivan Neretin
4 hours ago
That's what I m asking why will some molecules move to another vessel to equalise it. As motion of molecules is random, it might happen that some molecules move to vessel at higher temperature.
â Loop Back
4 hours ago
1
Of course they will. You are right, the motion of molecules is pretty random; also, there is quite a lot of them. How can we tell which way the net flow will be? We can't, unless we are able to find a measure. Luckily, some guys did that for us. The measure is called pressure.
â Ivan Neretin
3 hours ago