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

University Physics Volume 2
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ISBN:9781938168161
Author:OpenStax
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Chapter2: The Kinetic Theory Of Gases
Section: Chapter Questions
Problem 56P: (a) If the partial pressure of water vapor is 8.05 torr, what is the dew point? (760 torr = I atm...
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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.
Transcribed Image Text: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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