Variation of molar specific heat capacity at constant volume $(C_{V})$ is shown as function of temperature $T$ for a diatomic gas. If for a certain amount of the considered gas internal energy in state C is 14 times the sum of internal energies in states A and B, find x.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is 106.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

In states A, B and C degree of freedom are experimentally deduced to be $f_{A} = 3, f_{B} = 5, f_{C} = 7$ , respectively.
As internal energy, $U = \frac{f}{2} n R T,$
Therefore internal energies in the three states are equal to
$\begin{array}{l} U_{A} = \frac{3}{2} n R T_{0} ..... (i) \\ U_{B} = \frac{5}{2} n R (10 T_{0}) ..... (ii) \\ U_{C} = \frac{7}{2} n R (x T_{0}) ...... (iii) \end{array}$
It is given that, $U_{C} = 14 (U_{A} + U_{B})$
$\Rightarrow \frac{7}{2} n R (x T_{0}) = 14 [\frac{3}{2} n R T_{0} + \frac{5}{2} n R (10 T_{0})]$
`[using Eqs. (i), (ii) and (iii)]
$\Rightarrow x = 106$