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Dotsolo - Physics Teacher Home Page
Heat and Temperature
[Haba dan Suhu]


Thermometers

Boyle's Law / Hukum Boyle

Heat From The Sun [Haba dari Matahari]

Internal Energy
[Tenaga Dalam ]


Thermodynamics Process
[Proses Termodinamik ]


Linear expansion [Pengembangan Linear ]

The First Law / Hukum Pertama

Real and Ideal Gas
Gas Sebenar dan Gas Unggul


Degree of freedom
Darjah Kebebasan


Assignment Guide / Panduan tugasan

Assignment Guide 1(a) / Panduan tugasan 1(a)

Molecule motion / gerakkan molekul

Triple Point / Takatigaan

Test questions discussion/Perbincangan soalan ujian

Motion - Velocity - time

Motion - Excercise
Any given molecule can change its energy in any of its "degrees of freedom". There is one degree of freedom per independent mode of motion, ie., translational (rigid "whole body" movement in the x, y or z directions), rotational (whole body rotation around one or two independent axes) or vibrational (oscillation of bond length or angle). We will idealize the atom as a pointlike, structureless object for these purposes. For instance:

moleculetranslationalrotationalbond lengthbond angle
C3000
O 23210
H 2 O3321

An atom, as a point object, cannot have rotational degrees of freedom: a point object has no dimension and hence no moment of inertia (nothing to rotate about an axis). Besides its three translational and one vibrational degrees of freedom, a diatomic molecule can only rotate rigidly about its center of mass, since it has no cross sectional dimension (a bond is idealized as having no thickness). For larger molecules, such as water, there can be an oscillation of the bond angle:

in addition to its two independent vibrational modes and its six rigid degrees of freedom (three translational, rotation around either bond and around the Hydrogen atom). In general, any molecule (with more than two atoms) has 6 degrees of rigid motion freedom, one degree of bond length vibrational freedom for every bond, and one degree of bond angle vibrational freedom for every atom connecting two other atoms. You can see that the number of degrees of freedom for large molecules can be very great indeed!

Sebarang molekul boleh mengubah tenaganya dalam sebarang darjah kebebasan. Ada satu darjah kebebasan bagi setiap satu mod gerakan yang bebas. Iaitu; Anjakan ( translational ) gerakan seluruh jasad dalam arah x,y atau z ), kitaran (rotational ) putaran seluruh jasad pada satu atau dua paksi bebas atau getaran ( vibrational ) getaran panjang ikatan atau sudut. Kita akan mengandaikan atom adalah seperti titik tanpa struktur untuk tujuan ini. COntohnya seperti dalam jadual di atas

Atom sebagai objek titik, tidak boleh mempunyai darjah kebebasan kitaran; objek titik tidak ada saiz dan dengan itu tidak ada moment inertia (tidak ada apa yang hendak berputar terhadap satu paksi). Bagi molekul diatomik ( molekul yang terdiri dari dua atom) Tiga arah anjakan dan satu arah getaran. Molekul diatomik hanya boleh berputar pada pusat jisimnya sahaja kerana tidak ada saiz keratan rentas. ( Ikatan di andaikan tidak ada ketebalan) Bagi molekul yang lebih besar seperti air, boleh terdapat getaran (oscillation) terhadap sudut ikatan.