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What is “fractional error” for the following formula? Z= 2/3 X2Y3 , X= 7m , Y= 4m, σx=0.2m , σy=0.1m σZ=?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter4: Nonlinear Oscillations And Chaos

Section: Chapter Questions

Problem 4.14P

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Debye Theory of Solids

In solid-state physics, debye theory is used to estimate the phonons contributing to the specific heat capacity in a solid. It explains that the specific heat is a consequence of the vibrations of the atomic lattice of the solid, which is in contrast to the Einstein model. In the Einstein model, solids are treated as independent, non-interacting quantum harmonic oscillators. This model clearly explains the low-temperature dependence of the heat capacity, which is proportional to T3. This is known as Debye T3 law.

Question

What is “fractional error” for the following formula?

Z= 2/3 X²Y³ , X= 7m , Y= 4m, σx=0.2m , σy=0.1m

σZ=?

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