Answer to Question #110666 in Classical Mechanics for Tanya Saini

Question

Q5.A system of N spin-1/2 particles, each with magnetic moment m, is in presence of a
magnetic field B. Initially, all the magnetic dipoles are oriented along the direction of the
magnetic field. If the energy of the system is increased by ΔE = + mB, what is the change
in entropy of the system?

Answer 1

As per the given question,

N spin-1/2

magnetic moment of each =m

Magnetic field =B

Increased in the energy of the system=+mB

Change in entropy=?

We know that single bohr frequency $\nu=\dfrac{E_i-E_f}{h}=\dfrac{\omega_o}{2\pi}$

now substituting

$(\nu)=\dfrac{2\pi mB}{h}$ N energy

We know that,

$H=\omega_o . S$

For one,

and $H|+>=+\dfrac{h\omega}{2} |+>$

$H|->=-\dfrac{h\omega}{2} |->$

So, change in entropy for N,

$Q= E=mB$

S$=\dfrac{dE}{dT}=\dfrac{NmB}{2}$