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can anybody tell me that how pressure is an intensive property but i think that at many place pressure gernation depends on mass..u can see that if there are two balls having mass 1kg and 2kg then how can both apply same pressure on a table....and also according to the definition of pressure it is force applying per unit area and foce depends on mass then how pressure is an intensive property...?
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That is not quite the way it is. The table deforms in a microscopic sense till the weight of the mass above is in equilibrium with the surface area in contact. Let us assume that the table is unyielding. Then the area is same but the mass has changed so the pressure on the table has changed.
The confusion comes in the way pressure is understood. If you take a gas or liquid, the pressure inside that mass (in a horizontal plane) is independent of the mass.
If you place a vertical wall inside the container, the pressure does not change. When we say pressure we mean pressure inside the mass. That is an intensive property.
The situation described by you does not apply here because you are talking of interaction between two masses.
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if
bioramani
That is not quite the way it is. The table deforms in a microscopic sense till the weight of the mass above is in equilibrium with the surface area in contact. Let us assume that the table is unyielding. Then the area is same but the mass has changed so the pressure on the table has changed.
The confusion comes in the way pressure is understood. If you take a gas or liquid, the pressure inside that mass (in a horizontal plane) is independent of the mass.
If you place a vertical wall inside the container, the pressure does not change. When we say pressure we mean pressure inside the mass. That is an intensive property.
The situation described by you does not apply here because you are talking of interaction between two masses.
is it applicable for solid or not?in case of solid if u have to apply pressure on a small mass then the value of this pressure will less than the value of pressure on a large quantity of mass,,,
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Solids follow Hooke's law till the elastic deformation. After that it is plastic deformation. In the case of solids it is called the stress with the same units as pressure.
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bioramani
Solids follow Hooke's law till the elastic deformation. After that it is plastic deformation. In the case of solids it is called the stress with the same units as pressure.
you mean to say that pressure is developed only in liquid and gases...in solid it is called stress...means the word"pressure is an intensive property "is valid only for liquid and gases...and in solid it is called stress which is independent of mass..am i right sir?
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Yes.You are correct.
Consider an iron rod two sq.cm., in area with one end fixed and the other end pulled by a force of 2 kg.
The stress at any cross section along the length will be 1kg/sq.cm. This is true whatever the length or even material of the rod. This is why it is called an intensive property.
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pressure and stress have the same unit, i.e N/m(square) .
the only difference is that while stress acts in only one direction, pressure acts in all the directions.
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bioramani
Yes.You are correct.
Consider an iron rod two sq.cm., in area with one end fixed and the other end pulled by a force of 2 kg.
The stress at any cross section along the length will be 1kg/sq.cm. This is true whatever the length or even material of the rod. This is why it is called an intensive property.
thanks sir for answering me because me and my frends both were so much confused at this topic....
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zaveri said that stress acts in only one direction ,can u illustrate more ?
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dhananjay pathak
zaveri said that stress acts in only one direction ,can u illustrate more ?
It is important to understand clearly what happens in various cases.
In the case of a fluid, it is contained in a vessel,which resists change. This is not the case with a solid. The solid has a defined shape. Take the case of a cylinder loaded axially. The cylindrical periphery is
not confined. It increases in diameter consistent with the mechanical strength of the material.
The situation changes if you confine the cylinder inside a very much stronger container. If that is done, and the cylinder is axially loaded, it cannot increase in diameter. The stress inside the cylinder will now increase throughout in all directions.
The confusion arises because the two systems of a confined fluid and a free solid are not identical. If they are made identical the behaviour will also be identical.
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t
bioramani
It is important to understand clearly what happens in various cases.
In the case of a fluid, it is contained in a vessel,which resists change. This is not the case with a solid. The isolid has a defined shape. Take the case of a cylinder loaded axially. The cylindrical periphery is not confined. It increases in diameter consistent with the mechanical strength of the material.
The situation changes if you confine the cylinder inside a very much stronger container. If that is done, and the cylinder is axially loaded, it cannot increase in diameter. The stress inside the cylinder will now increase throughout in all directions.
The confusion arises because the two systems of a confined fluid and a free solid are not identical. If they are made identical the behaviour will also be identical.
thank u sir, that means stress directions are depends on the application of how and where the load is applied
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Sir..
while defining pressure is it assumed that molecules of a substance are uniformly distributed?
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Yes, that is assumed.
A curious phenomenon happens in particulate matter. When a heap of particulate matter say wheat, dry sand or salt is formed, it assumes a conial shape with a definite base angle. This will be very small for things like ragi and mustard while it can be high for sand. Tan(base angle) is the coefficient of internal friction for such aggregates.
If a cylinder is filled with such powder and a load applied to the top, the pressure decreases as you go down the tube and becomes zero for a L/D ratio > Tan(base angle).
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A.V.Ramani
Yes, that is assumed.
A curious phenomenon happens in particulate matter. When a heap of particulate matter say wheat, dry sand or salt is formed, it assumes a conial shape with a definite base angle. This will be very small for things like ragi and mustard while it can be high for sand. Tan(base angle) is the coefficient of internal friction for such aggregates.
If a cylinder is filled with such powder and a load applied to the top, the pressure decreases as you go down the tube and becomes zero for a L/D ratio > Tan(base angle).
thank q for clearing the pressure concept sir
was struck there too can you expand this more i still didn't got it
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A.V.Ramani
Yes.You are correct.
Consider an iron rod two sq.cm., in area with one end fixed and the other end pulled by a force of 2 kg.
The stress at any cross section along the length will be 1kg/sq.cm. This is true whatever the length or even material of the rod. This is why it is called an intensive property.
A.V.Ramani
It is important to understand clearly what happens in various cases.
In the case of a fluid, it is contained in a vessel,which resists change. This is not the case with a solid. The solid has a defined shape. Take the case of a cylinder loaded axially. The cylindrical periphery is not confined. It increases in diameter consistent with the mechanical strength of the material.
The situation changes if you confine the cylinder inside a very much stronger container. If that is done, and the cylinder is axially loaded, it cannot increase in diameter. The stress inside the cylinder will now increase throughout in all directions.
The confusion arises because the two systems of a confined fluid and a free solid are not identical. If they are made identical the behaviour will also be identical.
sir suppose I am able to cram more molecules of gas in the same space then the pressure will increase keeping the vol const by PV=nRT suggesting pressure is intensive only keeping vol const
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Kaustubbh
sir suppose I am able to cram more molecules of gas in the same space then the pressure will increase
Sure. You are right.
In this case, V is constant but you are increasing n by adding more molecules. P will increase proportionately.
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It is one of those answers that still doesn't intuitively make sense to me.
If the pressure increases proportionately with the number of moles (hence mass) in a fixed volume (and temperature of the system), how is it not an external property?
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Shashank Moghe
the number of moles (hence mass) in a fixed volume (and temperature of the system), how is it not an external property?
Density is an intensive property though it is the ratio of two extensive properties, mass and volume. By adding more moles to the same volume, the density has changed. But if the density were to be constant, the volume would have proportionately increased and the pressure would have remained the same.
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That clarifies things so much! Thank you. I suppose, pressure is independent of mass of the system as long as we have the ability to change the volume appropriately.
That is still such a difficult thing to wrap my head around - the boundaries for definitions seem to be so blur. Sometimes I feel so dumb, more so when I try to imagine the most basic definitions.
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Sir, like my system is a gas and as i increase the number of moles of gas, keeping volume, temp constant. Pressure will increase. Therefore, according to this logic - pressure depends on the amount of substance present in the system and therefore it is an extensive property. where is my logic wrong? i am confused..
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Consider a room and an open jar in the room. Now close the jar. The pressure inside the jar is the same as the pressure in the room though the amount of air in the room is 100000 times the amount of air in the jar.
If you now take a syringe and try to put in more air into the jar, which is already full of air, the air inside has to compress itself to a smaller volume to accommodate the extra air coming in. When you compress the air its pressure necessarily has to go up. On the other hand if you keep the jar open and place another jar of the same size mouth to mouth you have doubled the amount of gas. However, the pressure remains the same.
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Sir, but are we talking about the pressure exerted by the system on the surroundings being intensive? if we are, then how come Total pressure= sum of partial pressures as this property is of extensive functions like internal energy,etc. We know that density is intensive, therefore we cannot write density of mixture of liquids is density of liquid A p+ density of liquid B. But, we can write internal energy of a mixture of ideal gases as sum of their individual internal energies, as internal energy being extensive property of the system. I am confused sir.... very much indeed..
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Aman Aloon
how come Total pressure= sum of partial pressures
What is partial pressure? It is the pressure exerted by gas 1 if it were to occupy the total available volume with no other gas present. The same for every other gas in the mixture. Since you have eliminated all other gases, this gas whose initial volume at total pressure P was V1 now expands to the full volume V. By gas law PxV1 =P1xV, where P1 is the partial pressure of gas 1.You can go on for other gases 2, 3, 4 etc.
Therefore, P= P1+P2+P3+P4...
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