Search any question & find its solution
Question:
Answered & Verified by Expert
If a gas has $n$ degrees of freedom, then the ratio of $\frac{C_p}{C_V}$ is
Options:
Solution:
2995 Upvotes
Verified Answer
The correct answer is:
$\frac{n+2}{n}$
For a gas with $n$ degree of freedom,
$\begin{aligned}
C_p & =\left(\frac{n}{2}+1\right) \cdot R \quad \text { and } C_V=\frac{n}{2} R \\
\Rightarrow \quad \frac{C_p}{C_V} & =\frac{\left(\frac{n}{2}+1\right) R}{\frac{n}{2} \cdot R}=\left(\frac{n+2}{n}\right)
\end{aligned}$
$\begin{aligned}
C_p & =\left(\frac{n}{2}+1\right) \cdot R \quad \text { and } C_V=\frac{n}{2} R \\
\Rightarrow \quad \frac{C_p}{C_V} & =\frac{\left(\frac{n}{2}+1\right) R}{\frac{n}{2} \cdot R}=\left(\frac{n+2}{n}\right)
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.