Chuong IV- Tinh Chat Nhiet Cua Chat Ran

Chng IV TNH CHAT NHIET CUA CHAT RAN

I. NHIET DUNG CUA CHAT RAN1. Nhiet dungTheo nh luat I cua nhiet ong lc hoc:dQ = dU dWTrong o:dQ : nhiet nangdU : noi nangdW : cong, dW = pdV

Nhiet dung cua vat ran: CVR = Cmang + CelectronNoi nang cua vat ran U: U = Umang + UelectronUmang = Nang lng toan phan cua goc nguyen t dao ong quanh nut mang Uelectron = Nang lng toan phan cua cac electron

Nhiet dung ang tch:

2. Ket qua thc nghiem oi vi chat in moi CV ~ T2 oi vi kim loai CV ~ T nhiet o phong (300oK): gia tr nhiet dung cua hau het cac chat co gia tr khong oi 3R = 3NkB = 6 cal/mol.o. nhiet o thap: Khi giam nhiet o nhiet dung giam ro ret va tien en gia tr CV = 0 khi T = 0Khi T tang : CV tang dan en gia tr khong oi 3R = 3NkB = 6 cal/mol.o ien moi C ~ T3Kim loai C ~ T vi 10-4cal/mol.o2

3. NHIET DUNG ANG TCH CUA MANG TINH THEL THUYET CO IENMo hnh1 hat nut 3 dao ong t ieu hoa.Tinh the N hat 3N dao ong t.Nang lng cua mot dao ong t:vi m2 = f = he so cua lc Hooke

Theo phan bo Boltzman: Khi can bang nhiet, nang lng trung bnh cua mot dao ong t:

Trien khai tnh toan:

Trong dao ong ieu hoa: ong nang trung bnh = the nang trung bnh

at x = u2 dx = 2udu(n) = (n-1) (n-1)

Nang lng cua he gom N hat (3N dao ong t ieu hoa):U = 3NkT Nhiet dung ang tch cua 1 mol: CV = 3NAk = 3R = 6 cal/mol.oVay: L thuyet co ien phu hp vi thc nghiem nhiet o cao, khong phu hp nhiet o thap.

L THUYET EINSTEIN Mo hnh : mot chat ran co N hat la tap hp cua 3N dao ong t ieu hoa oc lap co cung tan so Nang lng cua moi dao ong t (1 lng t) En = nh vi n la so nguyen.Nang lng trung bnh cua mot dao ong t la:

L thuyet Einstein cho phep giai thch CV khong oi nhiet o cao, nhiet o thap CV giam khi nhiet o giam nhng giam nhanh hn ket qua thc nghiem.* nhiet o thap: kT > 1:

L THUYET DEBYEMO HNHChat ran gom cac dao ong t; mot dao ong t khong bieu th dao ong cua tng goc nguyen t nh mau cua Einstein ma bieu th cho dao ong chuan cua toan tinh the.Tinh the co N nguyen t th co 3N dao ong chuan: N dao ong doc va 2N dao ong ngang.Nang lng trung bnh cua mot dao ong t vi tan so la:

Tinh the la mot moi trng tan sac He thc tan sac: = qv Nang lng cua mang tinh the chat ran la:

Tinh the hu han co cac canh Lx, Ly, Lz. ieu kien bien vong cho ham song: exp[iq(r + L)] = expiqrVi nx, ny, nz Z

Trng hp n gianTinh the lap phng canh L Moi trng ang hng.Van toc truyen cac song lay trung bnh la vo. He thc tan sac:

Xet trong khong gian q Cac gia tr c phep cua q xac nh v tr cac nut cua mang. V = the tch cua tinh the, V = L3.

So cac gia tr c phep cua q bang so dao ong t co so song t 0 q:So cac dao ong t co tan so t 0 :

Vi q = So dao ong t co gia tr q trong khoang q q + dq:(1) va (2) : goi la ham mat o trang thai (mat o mode dao ong).

Dung gia tr trung bnh cua van toc theo cong thc:

max : tan so cc ai cua dao ong chuan, c tnh t:

U = 3NkT : trung vi ket qua co ien.

CV ~ T3 phu hp vi thc nghiem. L thuyet Debye trung vi ket qua thc nghiem ca nhiet o cao vi nhiet o thap.

Tnh chat hat ac trng bi nang lng photon = h II. L THUYET PHONON VE NHIET DUNGAnh sang co lng tnh: Tnh chat song ac trng bi bc songhay xung lng

Tng t, s lng t hoa cua song an hoi trong tinh the la phonon co nang lng va xung lng.S lng t hoa song anh sang la photon.Photon co the ton tai trong chan khong, nhng phonon ch co trong cac moi trng co the truyen song an hoi.

nhiet o xac nh, so phonon coi nh xac nh.

So phonon trong the tch V:

* nhiet o thap: Ly thuyet phonon ve nhiet dung phu hp vi ket qua thc nghiem.

TOM LAITinh the chat ran co the coi nh la mot hop cha kh phonon co so phonon thay oi theo nhiet o cua chat ran.Phonon va photon eu tuan theo phan bo Bose Einstein va c goi la cac hat Boson.

III. S DAN NHIET VA N NHIET CUA CHAT RANTrong cac vat ran ien moi qua trnh dan nhiet chu yeu la do cac phonon.Theo thuyet ong hoc chat kh: He so dan nhiet trong chat kh la:

CV : nhiet dung cua mot n v the tch kh.S DAN NHIET

Trong chat ran: Coi nh mot hop cha kh phononDebye a dung cong thc tren cho tinh the, vi:CV : nhiet dung cua mang tinh the.+ Tan xa hnh hoc: Tan xa tren mat tinh the, sai hong, + Tan xa phonon phonon.

Quang ng t do trung bnh p cua phonon t le nghch vi nong o phonon np va tiet dien tan xa hieu dung p: Nhiet o cao ( T >> D): K se giam khi nhiet o tang. Phu hp nh tnh vi ket qua thc nghiem.

S N NHIETCoi mang tinh the nh mot he cac dao ong t (DT) dao ong ieu hoa. Khi nhiet o tang bien o dao ong cua cac DT tang Khoang cach gia cac nguyen t tang N nhiet.Nhng phep tnh toan chnh xac cho ta ket qua he so n nhiet CV nhiet o cao: CV = const = const khong phu thuoc vao nhiet o. nhiet o thap: CV T3 T3.