A uniform pressure P is exerted on all sides of a solid cube at toc, by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? $$(K$$ is bulk modulus and α is coefficient of linear expansion?

Question

A uniform pressure P is exerted on all sides of a solid cube at  toc, by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? $$(K$$ is bulk modulus and α  is coefficient of linear expansion?

Infinity Learn · Accepted Answer

bulk modullus of a material is $$K=P$$ΔVV ;  here P is pressure, ΔV is change in volume, V is initial volume Δ$$VV=PK$$.........(1)  coefficient of linear expansion is α$$=$$Δll.ΔT  ; here Δl change in length; l is initial length; ΔT is change in temperature coefficient of volume expansion is γ$$=3$$α ΔVVΔ$$T=3$$.α Δ$$VV=3$$.α.ΔT substitute $$eqn(1)$$ $$PK=3$$.α.ΔT Δ$$T=P3K$$α

A uniform pressure P is exerted on all sides of a solid cube at $t^{o} c$ , by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? (K is bulk modulus and $α$ is coefficient of linear expansion?

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A uniform pressure P is exerted on all sides of a solid cube at toc, by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? (K is bulk modulus and α is coefficient of linear expansion?

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Ready to Test Your Skills?

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A uniform pressure P is exerted on all sides of a solid cube at $t^{o} c$ , by what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? (K is bulk modulus and $α$ is coefficient of linear expansion?