4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated, say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient itself either in the same direction, ↑, or opposed to,t, the field. The energy of a dipole is -µH if oriented with the field, and + µH if oriented against the field. Let N be the number of 4 states and M – N the number of ↑ states. For a given value of N, the total energy is μΗΝ- μΗ(M-) - (2Ν -M)μΗ The total magnetic moment I is I= (M-2N)µ where N'is the average value of N for a given M, H, and T. The work necessary to increase H by dH is – IdH. Find the specific heat C and the total magnetic moment for this system

4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated, say, with electron or nuclear spins). When placed in a magnetic field H, each dipole can orient itself either in the same direction, ↑, or opposed to,t, the field. The energy of a dipole is -µH if oriented with the field, and + µH if oriented against the field. Let N be the number of 4 states and M – N the number of ↑ states. For a given value of N, the total energy is μΗΝ- μΗ(M-) - (2Ν -M)μΗ The total magnetic moment I is I= (M-2N)µ where N'is the average value of N for a given M, H, and T. The work necessary to increase H by dH is – IdH. Find the specific heat C and the total magnetic moment for this system