We see that Einstein’s formula acco

We see that Einstein’s formula accounts for the decrease of heat capacity at low temperatures.
The physical reason for this success is that at low temperatures only a few oscillators possess enough energy to oscillate signiﬁcantly so the solid behaves as though it contains far fewer atoms than is actually the case. At higher temperatures, there is enough energy available for all the oscillators to become active: all 3N oscillators contribute, many of their energy levels are accessible, and the heat capacity approaches its classical value.
Figure 7.8 shows the temperature dependence of the heat capacity predicted by the Einstein formula.
The general shape of the curve is satisfactory, but the numerical agreement is in fact quite poor.
The poor ﬁt arises from Einstein’s assumption that all the atoms oscillate with the same frequency, whereas in fact they oscillate over a range of frequencies from zero up to a maximum value, νD.
This complication is taken into account by averaging over all the frequencies present, the ﬁnal result being the Debye formula:

We see that Einstein’s formula accounts for the decrease of heat capacity at low temperatures.
The physical reason for this success is that at low temperatures only a few oscillators possess enough energy to oscillate signiﬁcantly so the solid behaves as though it contains far fewer atoms than is actually the case. At higher temperatures, there is enough energy available for all the oscillators to become active: all 3N oscillators contribute, many of their energy levels are accessible, and the heat capacity approaches its classical value.
Figure 7.8 shows the temperature dependence of the heat capacity predicted by the Einstein formula. 
The general shape of the curve is satisfactory, but the numerical agreement is in fact quite poor. 
The poor ﬁt arises from Einstein’s assumption that all the atoms oscillate with the same frequency, whereas in fact they oscillate over a range of frequencies from zero up to a maximum value, νD. 
This complication is taken into account by averaging over all the frequencies present, the ﬁnal result being the Debye formula:

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We see that Einstein’s formula accounts for the decrease of heat capacity at low temperatures.The physical reason for this success is that at low temperatures only a few oscillators possess enough energy to oscillate signiﬁcantly so the solid behaves as though it contains far fewer atoms than is actually the case. At higher temperatures, there is enough energy available for all the oscillators to become active: all 3N oscillators contribute, many of their energy levels are accessible, and the heat capacity approaches its classical value.Figure 7.8 shows the temperature dependence of the heat capacity predicted by the Einstein formula. The general shape of the curve is satisfactory, but the numerical agreement is in fact quite poor. The poor ﬁt arises from Einstein’s assumption that all the atoms oscillate with the same frequency, whereas in fact they oscillate over a range of frequencies from zero up to a maximum value, νD. This complication is taken into account by averaging over all the frequencies present, the ﬁnal result being the Debye formula:

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Kita melihat bahwa rumus Einstein menyumbang penurunan kapasitas panas pada suhu rendah.
Alasan fisik untuk sukses ini adalah bahwa pada suhu rendah hanya beberapa osilator memiliki energi yang cukup untuk berosilasi secara signifikan sehingga berperilaku padat seolah-olah itu mengandung atom jauh lebih sedikit daripada benar-benar terjadi. Pada suhu yang lebih tinggi, ada energi yang cukup tersedia untuk semua osilator untuk menjadi aktif: semua osilator 3N berkontribusi, banyak dari tingkat energi mereka dapat diakses, dan kapasitas panas mendekati nilai klasik.
Gambar 7.8 menunjukkan ketergantungan suhu kapasitas panas diprediksi dengan rumus Einstein.
Bentuk umum dari kurva memuaskan, tetapi kesepakatan numerik sebenarnya sangat miskin.
Orang miskin fi t muncul dari asumsi Einstein bahwa semua atom berosilasi dengan frekuensi yang sama, padahal mereka terombang-ambing selama rentang . frekuensi dari nol sampai nilai maksimum, νD
Komplikasi ini diperhitungkan dengan rata-rata atas semua frekuensi ini, hasil nal fi menjadi rumus Debye:

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