Question

Define law of equipartition of energy Find Cp & Cv for monatomic gas​

Answer 1

Answer:

we see that, for a monatomic ideal gas: CV = (3/2)R. For diatomic and polyatomic ideal gases we get: diatomic: CV = (5/2)R. polyatomic: CV = 3R.

Answer 2

The law of equipartition of energy states that:

“Total energy of a gas molecule is equally distributed among all the degrees of freedom."

• For each degree of freedom, the share of energy is KT/2, where K is the boltzmann constant.

• This law is applicable for any dynamic system in thermal equilibrium.

Cp for a monatomic gas is calculated as follows:

• Q = nCpT                    (from first law of thermodynamics)     eq(1)

• Also, Q = E + W                                                                        eq(2)

• At constant pressure W = P(V2-V1) = nRT

• Therefore, E =(3/2)nRT

• Now, substituing the values of E and W in eq(2), we get,

       Q = (3/2)nRT + nRT

           = (5/2)nRT                                                                             eq(3)

• Upon comparing eq(1) and eq(3)

        Cp =(5/2) R

Cv for a monatomic gas is calculated as follows:

• Q = nCvT  (According to first law of thermodynamics)          eq(1)

• Also, Q = E + W                                                                         eq(2)  

• At constant volume, work done =0

• Therefore, E = (3/2) nRT

• Now, substituting the value of E in eq(2) we get,

        Q = (3/2) nRT                                                                            eq(3)

• Upon comparing eq(1) and eq(3)

        Cv =(3/2) R