One mole of a monatomic gas (C v = 3R/2) is mixed with two moles of a diatomic gas (C v = 5R/2). The molar specific heat at constant volume of the mixture is:

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One mole of a monatomic gas (Cv = 3R/2) is mixed with two moles of a diatomic gas (Cv = 5R/2). The molar specific heat at constant volume of the mixture is:

Answer: 13R/6.

A 13R/6
B 2R
C 5R/2
D 11R/6

Correct answer: A. 13R/6

Explanation: Cv,mix = (n1Cv1 + n2Cv2)/(n1+n2) = (1.5R + 5R)/3 = 6.5R/3 = 13R/6.

Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed v_p slightly less than the average v_avg, which is slightly less than the root-mean-square speed v_rms used in the pressure formula.

Concept context

Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.

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One mole of a monatomic gas (C<sub>v</sub> = 3R/2) is mixed with two moles of a diatomic gas (C<sub>v</sub> = 5R/2). The molar specific heat at constant volume of the mixture is:

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