Consider the phase change for iron from solid to liquid...

Consider the phase change for iron from solid to liquid forms. (a) How many degrees of freedom does each iron atom have in the solid state? (b) After it has melted? (c) Did the number of degrees of freedom of the conduction electrons change? (d) Did the number of degrees of freedom of the whole system increase or decrease? (e) On a microscopic scale, what happens to the energy put into the iron to melt it?

Consider the phase change for iron from solid to liquid forms.
(a) How many degrees of freedom does each iron atom have in the solid state?
(b) After it has melted?
(c) Did the number of degrees of freedom of the conduction electrons change?
(d) Did the number of degrees of freedom of the whole system increase or decrease?
(e) On a microscopic scale, what happens to the energy put into the iron to melt it?

Transcript

00:03 For the metal crystal, we can draw the picture like this way.

00:13 This is atom.

00:18 This is an atom.

00:21 So, between the atom, we have a simple virtual spring between the atom.

00:31 So for this atom, this center atom, we have the property, we can move this way and this way, the three way.

00:44 Along the xx, x, x, x, or z.

00:51 We can move the three directions, x, y, z direction.

00:54 And each direction has the properly has the kinetic energy and also has the potential energy.

01:09 So each direction have two energy, connecting and potential.

01:15 That means each energy has the energy has the one freedom.

01:23 So the total degree of freedom for this metal crystallitis has three.

01:32 Each direction has two, three directions, that means we have six.

01:37 And from equipartition, energy theory, we understand each freedom has one, has high kbt, internal energy.

01:50 So, one particle, because we have six freezes, that means we have six times half kbt, that means we have three kbt, internal energy for one atom.

02:14 So, therefore, for part a, we want to find out the specific heat to three r.

02:29 Pull it so we can start from the total internal energy the total internal energy will be we have n atoms each atoms for the 6 degree of freedom that means we have 3 kb and we can rewrite this one we will rewrite the kb to be the r over an a have a gorgeous number and the and then this could be the 3 n r t because n over n n is equal to n because we know n equal to n over n a so this equation could be the 3 n r and also could be the n 3r t we know for the we know for the internal energy we have the ncvt.

03:48 For the gas we have ncvt.

03:50 That means we can say that cv is equal to 3r.

03:59 Now for this case we are in the metal crystal lattice so we can ignore the constant pressure and constant value smaller specific heat so we can just write the c is 3r.

04:20 So this is the answer for part a.

04:26 We prove that c is 3r.

04:31 Now for part b, we already know c is 3r, which is equal to 3 times a .31, which is equal to 24 .0.

04:51 The unit is dual, more, per celsius.

04:59 Now, we know if this 3r is suitable for all the metal, we need to check it.

05:09 First, we check it for the island...

Please give Ace some feedback