Given that
The molar specific heat of a gas as given from the kinetic theory is $\frac{5}{2} R$ As we know that
$C _{ v }=\frac{ fR }{2} \text { and } C _{ p }=\left(1+\frac{ f }{2}\right) R$
where $f$ is the degree of freedom and $R$ is gas constant
Case $1:$
If the given specific heat is $C _v$, then $f =5$ then the gas will rigid diatomic
Case $2:$
If the given specific heat is $C _p$, then $f =3$
Then the gas will be monoatomic
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They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
| Student | Length of the pendulum $(cm)$ | Number of oscillations $(n)$ | Total time for $(n)$ oscillations $(s)$ | Time period $(s)$ |
| $I.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $II.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $III.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,