Bulk modulus of rigidity is zero. Can anyone explain why?
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Fluids (both liquids and gases) have a bulk modulus but no shear modulus. This may seem surprising that a whole class of materials would have a nonzero resistance to one kind of deformation but no resistance to another kind of deformation. However, the crucial difference between a bulk modulus and a shear modulus is that bulk deformation involves a change in volume while shear deformation does not.
Having no shear stress means that even an arbitrarily small shear force can cause a fluid to flow. For example, for a fluid in a square box, any arbitrarily small force can cause the top of the box to slide to the left, turning it into a parallelogram, if we ignore any resistance provided by the box itself. This is possible because microscopically the fluid consists of molecules that are sampling different configurations as they move around due to thermal energy. The microscopic configurations available to molecules in a parallelogram box are statistically indistinguishable from those in a square box, so there is no thermodynamic force that resists the shear deformation.
In contrast, having no bulk modulus would mean that an arbitrarily small compressive force could cause a fluid to shrink, e.g. we could shrink a box of fluid without any resistance from the fluid. However, compressing a fluid increases the average concentration of the fluid molecules, forcing the molecules closer together into configurations that are not statistically indistinguishable from their original configurations. The fluid molecules resist this change, pushing back to try to restore their initial equilibrium configuration. This resistance is what we measure when we measure a fluid’s bulk modulus.
It is also interesting to consider the microscopic reasons that solids do always have a nonzero shear modulus. Solids have long-range order. In the most idealized description, the atoms of a crystal are arranged in an ordered pattern that stretches all the way across a material. If a solid is in a square shape, it cannot be slowly stretched into a parallelogram without either (1) deforming the microscopic arrangements of atoms in a similar way throughout the crystal (e.g. four atoms forming a square being deformed into a parallelogram) or (2) ripping the crystal apart and sliding it at grain boundaries (think of an earthquake fault). Either of these processes require atoms to move into nonequilibrium configurations, so they resist shear deformation with a force that is measured by the shear modulus.
MARK BRAINLIEST...
Having no shear stress means that even an arbitrarily small shear force can cause a fluid to flow. For example, for a fluid in a square box, any arbitrarily small force can cause the top of the box to slide to the left, turning it into a parallelogram, if we ignore any resistance provided by the box itself. This is possible because microscopically the fluid consists of molecules that are sampling different configurations as they move around due to thermal energy. The microscopic configurations available to molecules in a parallelogram box are statistically indistinguishable from those in a square box, so there is no thermodynamic force that resists the shear deformation.
In contrast, having no bulk modulus would mean that an arbitrarily small compressive force could cause a fluid to shrink, e.g. we could shrink a box of fluid without any resistance from the fluid. However, compressing a fluid increases the average concentration of the fluid molecules, forcing the molecules closer together into configurations that are not statistically indistinguishable from their original configurations. The fluid molecules resist this change, pushing back to try to restore their initial equilibrium configuration. This resistance is what we measure when we measure a fluid’s bulk modulus.
It is also interesting to consider the microscopic reasons that solids do always have a nonzero shear modulus. Solids have long-range order. In the most idealized description, the atoms of a crystal are arranged in an ordered pattern that stretches all the way across a material. If a solid is in a square shape, it cannot be slowly stretched into a parallelogram without either (1) deforming the microscopic arrangements of atoms in a similar way throughout the crystal (e.g. four atoms forming a square being deformed into a parallelogram) or (2) ripping the crystal apart and sliding it at grain boundaries (think of an earthquake fault). Either of these processes require atoms to move into nonequilibrium configurations, so they resist shear deformation with a force that is measured by the shear modulus.
MARK BRAINLIEST...
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