A gas has molar heat capacity `C = 37.55 J "mole"^(-1)K^(-1)`, in the process PT = constant, find the number of degree of freedom of the molecules of the gas.

Options

A. 6
B. 3
C. 1
D. 5

Answer

D

Explanation

Here, `C=37.55J "mole" ^(-1)K^(-1),andPT=K`(constant)
According to standard gas equation
PV = RT or P = RT/V
From `(i),(RT)/(V)xxT=Kor V=(RT^(2))/(K)`
`therefore(dV)/(dT)=(2RT)/(K)`
But `T/K=1/P` from eqn. (i), therefore, `(dV)/(dT)=(2R)/(P)" "...(ii)`
As, `C=C_(v)+P(dV)/(dT),` therefore, using (ii)
`C=C_(v)+Pxx(2R)/(P)=C_(v)+2Ror C_(V)=C2R`
As, `C_(v)=n/2R`
`thereforen/2R=C-2Ror n =(2(C-2R))/(R)=(2(37.55-2xx8.3))/(8.3)=5`