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Based on the principle of equipartition of energy, the mo lar heat capacity of CO2 at constant volume Cv,m is:
- a)3.5 R
- b)6 R
- c)6.5 R
- d)9 R
Correct answer is option 'C'. Can you explain this answer?
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Equipartition of Energy Principle
The equipartition of energy principle states that in thermal equilibrium, the total energy of a molecule is distributed equally among all its degrees of freedom. Each degree of freedom contributes 0.5 kT to the total energy of the molecule, where k is the Boltzmann constant and T is the temperature.
Molar Heat Capacity of CO2 at Constant Volume
The molar heat capacity of a substance at constant volume (Cv,m) is the amount of heat required to raise the temperature of one mole of the substance by one degree Celsius at constant volume. According to the equipartition of energy principle, each molecule of CO2 has three degrees of freedom, corresponding to the three translational modes of motion.
Therefore, the molar heat capacity of CO2 at constant volume can be calculated as follows:
Cv,m = 3/2R
where R is the universal gas constant. Substituting the value of R (8.314 J/mol.K) gives:
Cv,m = (3/2) x 8.314 J/mol.K = 12.47 J/mol.K
However, experimental observations show that the molar heat capacity of CO2 at constant volume is actually lower than this theoretical value. This is because CO2 molecules also have two vibrational modes of motion, which can store and release energy at certain frequencies that depend on the molecule's structure and composition.
At room temperature, the vibrational modes of CO2 are not excited enough to contribute significantly to the molar heat capacity at constant volume. However, at higher temperatures or in the presence of infrared radiation, the vibrational modes of CO2 can become excited and contribute to the molar heat capacity.
Therefore, the correct answer is option C (6.5 R), which takes into account both the translational and vibrational modes of motion of CO2 molecules.
The equipartition of energy principle states that in thermal equilibrium, the total energy of a molecule is distributed equally among all its degrees of freedom. Each degree of freedom contributes 0.5 kT to the total energy of the molecule, where k is the Boltzmann constant and T is the temperature.
Molar Heat Capacity of CO2 at Constant Volume
The molar heat capacity of a substance at constant volume (Cv,m) is the amount of heat required to raise the temperature of one mole of the substance by one degree Celsius at constant volume. According to the equipartition of energy principle, each molecule of CO2 has three degrees of freedom, corresponding to the three translational modes of motion.
Therefore, the molar heat capacity of CO2 at constant volume can be calculated as follows:
Cv,m = 3/2R
where R is the universal gas constant. Substituting the value of R (8.314 J/mol.K) gives:
Cv,m = (3/2) x 8.314 J/mol.K = 12.47 J/mol.K
However, experimental observations show that the molar heat capacity of CO2 at constant volume is actually lower than this theoretical value. This is because CO2 molecules also have two vibrational modes of motion, which can store and release energy at certain frequencies that depend on the molecule's structure and composition.
At room temperature, the vibrational modes of CO2 are not excited enough to contribute significantly to the molar heat capacity at constant volume. However, at higher temperatures or in the presence of infrared radiation, the vibrational modes of CO2 can become excited and contribute to the molar heat capacity.
Therefore, the correct answer is option C (6.5 R), which takes into account both the translational and vibrational modes of motion of CO2 molecules.
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Based on the principle of equipartition of energy, the mo lar heat capacity of CO2 at constant volume Cv,m is:a)3.5 Rb)6 Rc)6.5 Rd)9 RCorrect answer is option 'C'. Can you explain this answer?
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