12. Compute a formula to show the correlation between the specific heat C, u(x,t) temperatureand Q(x,t) internal energy per unit volume of the 1 dimension metal bar. (With the assistantof this formula q(x,t)=-ko, q: vector field that present the magnitude and dimension ofheat flow.12.b By applying the conservation of energy prove this formula with the assistant of thisformula:f (x + Ax, t) = f(x, t) + A (x, t))aQ agat ax;hence to apply the 2d PDES (partial differential equation) to find the temperature (x,t)12.c Using the guess T(x,t)=x(u)U(t) to prove that it is separable into two formula. (A as constant)du1.d²x2.dx12.d Guess the temperature distribution T(x, co) of an imaginary 1 dimension metal bar that isinfinity long(-oo< x< 00); 12.e hence to find the sign-A for the time dependent differential equation.

We know that We considering the temperature in a one-dimensional bar of length L. We assume that the…

Compute a formula to show the correlation between the specific heat C, u(x,t) temperature and Q(x,t) internal energy per unit volume of the 1 dimension metal bar. (With the assistant of this formula q(x,t)=-k, q: vector field that present the magnitude and dimension of

Compute a formula to show the correlation between the specific heat C, u(x,t) temperature and Q(x,t) internal energy per unit volume of the 1 dimension metal bar. (With the assistant of this formula q(x,t)=-k, q: vector field that present the magnitude and dimension of

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

12. Compute a formula to show the correlation between the specific heat C, u(x,t) temperature
and Q(x,t) internal energy per unit volume of the 1 dimension metal bar. (With the assistant
of this formula q(x,t)=-ko, q: vector field that present the magnitude and dimension of
heat flow.
12.b By applying the conservation of energy prove this formula with the assistant of this
formula:f (x + Ax, t) = f(x, t) + A (x, t))
aQ ag
at ax
;hence to apply the 2d PDES (partial differential equation) to find the temperature (x,t)
12.c Using the guess T(x,t)=x(u)U(t) to prove that it is separable into two formula. (A as constant)
du
1.
d²x
2.
dx
12.d Guess the temperature distribution T(x, co) of an imaginary 1 dimension metal bar that is
infinity long(-oo< x< 00); 12.e hence to find the sign-A for the time dependent differential equation.

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