AP EAPCET 04-Jul-2022 Shift 2 Paper

In non-rigid diatomic molecule with an additional vibrational mode, each molecule has additional energy equal to 2×‌

1

2

kBT=kBT, becausea vibrational frequency has both kinetic and potential energy modes.
∴‌‌U=(‌

5

2

kBT+kBT)NA=‌

7

2

kBNAT
‌=‌

7

2

RT‌‌‌‌‌‌‌‌‌‌[R=kBNA]
∴‌‌CV‌=‌

dU

dT

=‌

d

dT

(‌

7

2

RT)=‌

7

2

R
Cp‌=CV+R=‌

7

2

R+R=‌

9

2

R
‌

Cp

CV

‌=‌

9∕2R

7∕2R

⇒‌

Cp

CV

=‌

9

7

⇒‌‌49Cp2‌=81CV2