Consider a paramagnetic system of N elementary dipoles (with dipole moment μ) that can only have ...
Consider a paramagnetic system of N elementary dipoles (with dipole moment μ) that can only have states of parallel ↑ or antiparallel ↓ to the applied magnetic field B. The energies associated with each dipole is ±μ-B, the lower energy state being when the dipole is parallel to the B field. The macrostate state of the system will be defined by Nt, or equivalently, the total energy: The multiplicity of a given macrostate of a paramagnet is given by: (a) For a system of 100 dipoles: (i) Calculate and plot the energy U/uB and entropy S/k of each macrostate of the system (ii) Plot the entropy S/k as a function of the energy UjuB (ii) Using a centred finite difference scheme, for each macrostate, calculate the dimensionless temperature kT/uE kT S+1-S-1) (iv) Plot the dimensionless temperature kTJuB as a function of U/NIB. Discuss your results including an interpretation of the sign of the dimensionless temperature (v) Using a centred finite difference scheme, calculate and plot the heat capacity C/Nk as a function of the sionless temperature kT/uB (b) Repeat for a system of 300 dipoles. Discuss any differences.
Consider a paramagnetic system of N elementary dipoles (with dipole moment μ) that can only have states of parallel ↑ or antiparallel ↓ to the applied magnetic field B. The energies associated with each dipole is ±μ-B, the lower energy state being when the dipole is parallel to the B field. The macrostate state of the system will be defined by Nt, or equivalently, the total energy: The multiplicity of a given macrostate of a paramagnet is given by: (a) For a system of 100 dipoles: (i) Calculate and plot the energy U/uB and entropy S/k of each macrostate of the system (ii) Plot the entropy S/k as a function of the energy UjuB (ii) Using a centred finite difference scheme, for each macrostate, calculate the dimensionless temperature kT/uE kT S+1-S-1) (iv) Plot the dimensionless temperature kTJuB as a function of U/NIB. Discuss your results including an interpretation of the sign of the dimensionless temperature (v) Using a centred finite difference scheme, calculate and plot the heat capacity C/Nk as a function of the sionless temperature kT/uB (b) Repeat for a system of 300 dipoles. Discuss any differences.