wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If a gas has n degrees of freedom ratio of specific heats of gas is?

A
1+n2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
1+1n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1+n2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1+2n
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 1+2n

Let us take 1 mole of the ideal gas at Kelvin temperature T. It has N molecules i.e. Avogadro's number. The internal energy of an ideal gas is only in the form of kinetic. The average KE per molecule of the ideal gas is

12nkT

Where k is Boltzmann constant,

n is the degree of freedom.

Therefore the internal energy of one mole of gas would be

E=N(12nKT)

Since k=RN

So, E=12nRT

Now specific heat at constant volume,

Cv=dEdT=n2R

And specific heat at constant pressure,

Cp=n2R+R=n+22R

Therefore, ratio of Cp and Cv will be

CpCv=n+22Rn2R

CpCv=n+22Rn2R

CpCv=1+2n

Thus option D is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Heat Capacity
CHEMISTRY
Watch in App
Join BYJU'S Learning Program
CrossIcon