Interpretation:
H2 gas has a single vibrational frequency of 1.295 x 1014 s-1. The vibrational contribution to the heat capacity, Cv (vib) versus temperature from 0 to 2000 K is to be plotted.
Concept introduction:
Generally, the vibrational partition function of a molecule is derived by incorporating the calculated vibrational energy values into the exponentials and found in notation of Cv (vib) and adding everything. heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T1 and T2 can be expressed as
Answer to Problem 2.92E
The vibrational partition function is given by Cv >(vib) =
Temperature (K) | Cv (vib) |
100 | ≈1 |
500 | ≈1 |
1000 | 1.00202 |
1500 | 1.016 |
2000 | 1.047 |
Explanation of Solution
Given,
The vibrational partition function is given by Cv (vib) =
Single vibrational frequency of hydrogen = 1.295 x 1014 s-1
We know that,
• Cv (vib) at 100 K:
Cv (vib) ≈1
• Cv (vib) at 500 K:
Cv (vib) ≈1
• Cv (vib) at 1000 K:
Cv (vib) = 1.002
• Cv (vib) at 1500 K:
Cv (vib) = 1.016
• Cv (vib) at 2000 K:
Temperature (K) | Cv (vib) |
100 | ≈1 |
500 | ≈1 |
1000 | 1.00202 |
1500 | 1.016 |
2000 | 1.047 |
Thus, the vibrational contribution to the heat capacity, Cv (vib) versus temperature from 0 to 2000 K is plotted.
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Chapter 2 Solutions
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