Does elasticity limit exist for a perfect gas? Are young's modulus and shear modulus inversely proportional to temperature and what about bulk modulus?
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$\begingroup$ Can you define what you mean by an "elasticity limit"? For an ideal gas, the Young's modulus and shear modulus are 0, and the bulk modulus is equivalent to the pressure. $\endgroup$– ChemomechanicsCommented May 15, 2018 at 5:13
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$\begingroup$ I think it means that whether an ideal gas can resist any permanent change or not. $\endgroup$– Izza AmnaCommented May 23, 2018 at 14:27
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2 Answers
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Per your definition, no elasticity limit exists for any gas, let alone an ideal gas. The elasticity limit or yield point arises in solids because the molecules are essentially fixed in place; permanent deformation under stress generally corresponds to (1) molecules slipping past each other as dislocations (i.e., line defects) move through the material or (2) crack formation as new surfaces are formed. In the gas, no fixed structure exists, and so the concept of stress-induced yield has no meaning.
(In addition, you can certainly cause a phase transition to a liquid or solid by compressing a gas, but the gaseous state is recovered at equilibrium once the pressure is removed.)
You also asked about the elastic moduli. The Young's modulus and shear modulus are zero for a gas because both moduli involve shear deformation, and a gas cannot sustain a shear stress. The isothermal bulk modulus $K=-V(\partial P/\partial V)_T$ can be easily derived to be $P$ for an ideal gas, for which the equation of state $PV=nRT$ applies. This equation of state also indicates that the bulk modulus $K=P$ scales linearly with temperature $T$ for a fixed amount $n$ of an ideal gas at constant volume $V$.
Is this the information you were looking for?
answered May 23, 2018 at 18:12
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$\begingroup$ Yes I got my answer. Thank you so much. You explained it really well (y) $\endgroup$ Commented May 24, 2018 at 6:34
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Elasticity limit is defined only for continuous media or materials undergoing irreversible deformation. An ideal gas does not undergo any internal irreversible transformation, when, confined in a container, is compressed or expanded.
