The molar specefic heat at constant volume Cv for diatomic gas is:
Correct answer: C. 5/2R
- A. 3/2R
- B. 7/2R
- C. 5/2R
- D. 9/2R
Explanation
The correct answer is Option C: 5/2R. This value is derived from the fact that diatomic gases have translational and rotational degrees of freedom, leading to a higher molar specific heat at constant volume compared to monatomic gases. Specifically, diatomic molecules have five degrees of freedom at room temperature, resulting in Cv = (5/2)R.Option A (3/2R) is the molar specific heat for monatomic gases, which only have three translational degrees of freedom. Option B (7/2R) assumes more degrees of freedom than a diatomic gas exhibits under typical conditions. Option D (9/2R) is even higher and incorrect, as it suggests even more degrees of freedom that don't apply to diatomic gases at constant volume.
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About Molar Specific Heat of a Gas
Molar specific heat is the heat required to raise the temperature of one mole of a gas by one kelvin, expressed through Q = nCΔT. Questions compare the constant volume value Cv with the constant pressure value Cp, apply the ideal gas relation Cp − Cv = R, and identify how the thermodynamic process affects heat capacity.
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