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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc17db0cd-a293-444f-916b-7ee3b8a51e85%2F08a1f5dc-2c83-4ee1-ac00-23aaf8fbdde1%2Fe7nbn5w_processed.jpeg&w=3840&q=75)
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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