%3Cp%3EA%20system%20contains%203%20spins%20in%20a%20line.%20Each%20of%20these%20

Question

%3Cp%3EA%20system%20contains%203%20spins%20in%20a%20line.%20Each%20of%20these%20are%3A%3C%2Fp%3E%0A%3Cp%3E%20%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(s_i%20%3D%20%5Cpm%201%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(i%20%3D%0A1%2C2%2C3%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3EThe%20hamiltonian%20for%20this%20system%20is%3A%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(H(s_1%2C%20s_2%2C%20s_3)%20%3D%0A-J(s_1%20s_2%20%2B%20s_2%20s_3)%20-%20h(s_1%20%2B%20s_2%20%2B%20s_3)%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E1)%20List%20the%20microscopic%20states%20of%20the%20systm%20and%20the%0Acorresponding%20energies%3C%2Fp%3E%0A%3Cp%3E2)%20Find%20the%20partiton%20function%20Z(T%2C%20h)%20of%20the%20canonical%20ensemble%0Aand%20write%20it%20in%20terms%20of%20sinh%20and%20cosh%20functions%3C%2Fp%3E%0A%3Cp%3E3)%20Find%20the%20magnitization%20first%20in%20terms%20of%20the%20partition%0Afunction%20then%20the%20explicit%20expressions%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(M(T%2C%20h)%20%3D%20%5Csum_%7Bi%7D%0As_i%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E4)%20Find%20heat%20capacity%20C%20at%20h%20%3D%200%3C%2Fp%3E%0A%3Cp%3E5)%20find%20the%20limiting%20values%20of%20energy%2C%20entropy%2C%20and%0Amagnetization%20in%20the%20limits%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(T%20%3D%200%20and%20h%20%3D%0A0%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(T%20%3D%200%0Aand%200%20%26lt%3B%20h%20%26lt%3B%26lt%3B%20J%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%0A%3Cspan%20class%3D%22finalized_jax%22%3E%5C(%20T%20%3D%200%20and%20J%20%26lt%3B%26lt%3B%20h%20%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(h%20%3D%200%20and%20J%0A%26lt%3B%26lt%3B%20kbT%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble%20smarterwiki-popup-bubble-active%20smarterwiki-popup-bubble-flipped%20c1%22%3E%0A%3Cspan%20class%3D%22smarterwiki-popup-bubble-body%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links-container%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links-row%22%3E%3Ca%20target%3D%22_blank%22%20title%3D%0A%22Search%20Wikipedia%22%20href%3D%0A%22http%3A%2F%2Fwww.google.com%2Fsearch%3Fhl%3Dcom%26amp%3BbtnI%3DI'm%2BFeeling%2BLucky%26amp%3Bq%3Dh%2520%253D%25200%2520and%2520J%2520%253C%253C%2520kbT%2Bwikipedia%22%0Aclass%3D%0A%22smarterwiki-popup-bubble-link%22%3E%3C%2Fa%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fp%3E%0A

Explanation / Answer

%3Cp%3EA%20system%20contains%203%20spins%20in%20a%20line.%20Each%20of%20these%20are%3A%3C%2Fp%3E%0A%3Cp%3E%20%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(s_i%20%3D%20%5Cpm%201%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(i%20%3D%0A1%2C2%2C3%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3EThe%20hamiltonian%20for%20this%20system%20is%3A%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(H(s_1%2C%20s_2%2C%20s_3)%20%3D%0A-J(s_1%20s_2%20%2B%20s_2%20s_3)%20-%20h(s_1%20%2B%20s_2%20%2B%20s_3)%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E1)%20List%20the%20microscopic%20states%20of%20the%20systm%20and%20the%0Acorresponding%20energies%3C%2Fp%3E%0A%3Cp%3E2)%20Find%20the%20partiton%20function%20Z(T%2C%20h)%20of%20the%20canonical%20ensemble%0Aand%20write%20it%20in%20terms%20of%20sinh%20and%20cosh%20functions%3C%2Fp%3E%0A%3Cp%3E3)%20Find%20the%20magnitization%20first%20in%20terms%20of%20the%20partition%0Afunction%20then%20the%20explicit%20expressions%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(M(T%2C%20h)%20%3D%20%5Csum_%7Bi%7D%0As_i%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E4)%20Find%20heat%20capacity%20C%20at%20h%20%3D%200%3C%2Fp%3E%0A%3Cp%3E5)%20find%20the%20limiting%20values%20of%20energy%2C%20entropy%2C%20and%0Amagnetization%20in%20the%20limits%3C%2Fp%3E%0A%3Cp%3E%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(T%20%3D%200%20and%20h%20%3D%0A0%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(T%20%3D%200%0Aand%200%20%26lt%3B%20h%20%26lt%3B%26lt%3B%20J%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%0A%3Cspan%20class%3D%22finalized_jax%22%3E%5C(%20T%20%3D%200%20and%20J%20%26lt%3B%26lt%3B%20h%20%5C)%3C%2Fspan%3E%0A%26nbsp%3B%26nbsp%3B%20%26nbsp%3B%26nbsp%3B%20%3Cspan%20class%3D%22finalized_jax%22%3E%5C(h%20%3D%200%20and%20J%0A%26lt%3B%26lt%3B%20kbT%5C)%3C%2Fspan%3E%20%26nbsp%3B%26nbsp%3B%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble%20smarterwiki-popup-bubble-active%20smarterwiki-popup-bubble-flipped%20c1%22%3E%0A%3Cspan%20class%3D%22smarterwiki-popup-bubble-body%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links-container%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links%22%3E%3Cspan%20class%3D%0A%22smarterwiki-popup-bubble-links-row%22%3E%3Ca%20target%3D%22_blank%22%20title%3D%0A%22Search%20Wikipedia%22%20href%3D%0A%22http%3A%2F%2Fwww.google.com%2Fsearch%3Fhl%3Dcom%26amp%3BbtnI%3DI'm%2BFeeling%2BLucky%26amp%3Bq%3Dh%2520%253D%25200%2520and%2520J%2520%253C%253C%2520kbT%2Bwikipedia%22%0Aclass%3D%0A%22smarterwiki-popup-bubble-link%22%3E%3C%2Fa%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fp%3E%0A Mechanical Engineering is it answer of your question!! :P :)

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.