(a) Using the potential energy formulation, = ∫0^L (1)/(2)k...

(a) Using the potential energy formulation, $\pi_T = \int_0^L \frac{1}{2}k \left(\frac{dT}{dx}\right)^2 dx - \int_0^L Q T dx + \frac{1}{2}h(T_L - T_\infty)^2$ Prove that the element conductivity matrix is: $[k_T] = \frac{k}{l_e} \begin{bmatrix} 1 & -1 \ -1 & 1 \end{bmatrix}$

Transcript

00:01 Hi, let's see n type semiconductor as all coefficient rh equal to 4 .16 into 10 to the power minus 4 v inverse mq.

00:14 And mobility of electron mu equal to 0 .38 meter square v inverse s inverse.

00:26 Now let's find whole concentration if n i equal to 2 .1 into 10 to the power.

00:34 19 m power minus 3.

00:40 According to law of mass action under thermal equilibrium the product of concentration of free electron and concentration of whole remains constant therefore we have n into p equal to n i square let's take this is equation 1 now relation between all coefficient and concentration of electron is rh equal to 1 by n e.

01:09 From this equation we'll write n equal to 1 by rh into e.

01:19 Now i'm going to substitute the value.

01:22 So 1 by rh is 4 .16 into 10 to the power minus 4 and e is 1 .6 into 10 to the power minus 19.

01:34 That is equal to 1 .5 into 10 to the power 22 per meter cube.

01:45 Now i'm going to substitute this n value in the equation number 1.

01:49 So i will be getting the n is 1 .5 into 10 to the power 22 into p equal to n i is 2 .1 into 10 to the power 19 the whole square.

02:10 So from here we can find the b value which is 2 .94 into 10 to the power 16 per meter cube.

02:24 Now let's find conductivity relation between mobility, conductivity and whole coefficient is given by mu equal to sigma rh.

02:37 Here mu is mobility, sigma is conductivity and rh is whole coefficient...

Question

(a) Using the potential energy formulation, $\pi_T = \int_0^L \frac{1}{2}k \left(\frac{dT}{dx}\right)^2 dx - \int_0^L Q T dx + \frac{1}{2}h(T_L - T_\infty)^2$ Prove that the element conductivity matrix is: $[k_T] = \frac{k}{l_e} \begin{bmatrix} 1 & -1 \ -1 & 1 \end{bmatrix}$

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