derive the energy eigenvalues for s state in three dimensional square well do all the steps 1003

Name: derive the energy eigenvalues for s state in three dimensional square well do all the steps 10035
Uploaded: 2021-12-19T14:24:40-08:00
Duration: 4 min 42 s
Channel: Manish Jain
Description: derive the energy eigenvalues for s state in three dimensional square well do all the steps 10035

Step 1: The potential energy inside the square well is zero, while outside the well it is infini

Derive the energy eigenvalues for s state in three...

Transcript

00:01 In this question we have given a pv diagram of the process that is a b c and we have to find the temperature of the gas at point a b and c so first of all i'm doing the given pv diagram for this tuition so this is our pressure axis and this is volume axis and this is the process a b and this is the process from b to c so this is a this is b and this is c we have given the volume at point a and that is 0 .01 and at b the volume is this is 0 .07 meter cube and the pressure at this point is 2 atmospheric and this point the pressure is 8 so this is our pressure axis this is our volume axis so first of all we have given the number of moles that is n is equal to 0 .45 moles now we have to find the temperature at point a b and c so we can say that from ideal gas equation or from gas equation that is pv is equals to nrt.

01:16 Now from here we get the value of temperature so this will come out to be pv divides by nr.

01:23 So in the first part of the problem the temperature at state a is given by that is pressure at a into volume at a upon n into r.

01:34 Now put all the data in this equation.

01:36 So this is 2 into 10 to the temperature.

01:38 Power 5 into this is 0 .01 upon 0 .45 into this is 8 .315 after solving this we get this is 535 kelvin so this is the temperature at a similarly we can find the temperature at state b and this is given by p b into vb upon this is n into r now put all the data in this equation so pressure at this is 5 into 10 to the power 5 into this is 0 .07 upon 0 .45 into 8 .315 and after solving this we get this is 9 350 kelvin.

02:18 Now temperature at c is given by this is pressure at c into volume at c upon this is n into r so this is 8 into 10 to the power 5 into 0 .07 upon 0 .45 into this is 8 .35 into this is 8 .315 and this will come out to be 15 ,000 kelvin.

02:40 So this is the temperature at state c.

02:43 This is temperature at b and this is temperature at a.

02:52 Now in the second part of the problem, we have to find the work done by or on the gas in this process...