A gas mixture is being created with two species of gas, and the second at room t

Question

A gas mixture is being created with two species of gas, and the second at room temperature T (approximately 293K).The first gas is monatomic helium, and the second gas is triatomic (three atoms)CO_2. Assuming that the molecules in the triatomic gas are many rotational degrees of freedom does it have? Assuming that molecular vibration of CO_2 is n0 molar specific heat at constant volume? Experimentally, the measured ratio gamma = C_p/C_v is found to be close to gamma meas =9/7,what can be inferred about the total numbers of degrees of freedom, f, in the CO_2 molecule. Estimate the specific heat at constant volume of the mixture, C_v,m if equal numbers of helium atoms and CO_2 Molecules are mixed.

Explanation / Answer

(a) The given data is the molecules of CO2 are arranged in a triangle.

Even though CO2 is arranged traingle mode in gas form, CO2 is a linear, triatomic molecule.

Hence, Total No. of degrees of freedom is 3N where N is the total number of atoms.

So we have total 9 degrees of freedom, Out of nine, CO2 has two rotational degrees of freedom.

One is along with axis which is touching all three atoms and another one is perpendicular to axis ie through Carbon atom.

(b) The specific heat of a molecule depends on the number of degrees of freedom the molecule has. There are several degrees of freedom available: translation (3), rotation (3), vibration (depends on the number of bonds in a molecule) and electronic modes.

Each degree of freedom contributes 1/2R worth of heat capacity.

in Case of CO2, we have 3 translations, 2 rotational and 3 vibrational degrees of freedom as per the formula 3N-5 in case of linear molecules.

Since we are considering heat capacity at constant volume and vibrations are not exited hence

Cv = (3 transitional + 2 rotational degrees of freedom)R/2 = 5R/2

(c) Total No. of degrees of freedom is 3N where N is the total number of atoms.

in case of CO2 we have three atoms, hence, total number of degrees of freedom are 3*3 = 9

It is also evidenced from = CP / CV = 9/7, incase of Cp all degrees of freedom are active as per experimentally measured value,

Hence in case of CO2 we have three atoms, hence, total number of degrees of freedom are 3*3 = 9

(d) Specific heat of the mixture, Cvm=n1Cv1+n2Cv2(n1+n2)

where n1 no. of molecules of He,

n2 no. of molecules of CO2, since no. of molecules of He and CO2 are same n1 = n2

Cv for He is NR/2 where, N is the total number of degrees of freedom for monoatomic gas like He

hence Cv for He is 3R/2,

As per above explanation to the previous answers Cv for CO2 is 5R/2

By substituting in the above equation, Cvm = 4R/2 = 2R

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.