MHT CET · Physics · Kinetic Theory of Gases
The ratio of the specific heats \(\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\) in terms of degrees of freedom 'n' is given by
- A \(\left(1+\frac{n}{2}\right)\)
- B \(\left(1+\frac{1}{n}\right)\)
- C \(\left(1+\frac{10}{3}\right)\)
- D \(\left(1+\frac{2}{n}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(1+\frac{2}{n}\right)\)
Step-by-step Solution
Detailed explanation
\(C_{v}=n \times \frac{R}{2} ;\)
\(C_{p}=C_{v}+R=\frac{n R}{2}+R=\left(\frac{n}{2}+1\right) R\)
\(\therefore \frac{C_{p}}{C_{v}}=\frac{\left(\frac{n}{2}+1\right) R}{\frac{n R}{2}}=\left(1+\frac{2}{n}\right) R\)
\(C_{p}=C_{v}+R=\frac{n R}{2}+R=\left(\frac{n}{2}+1\right) R\)
\(\therefore \frac{C_{p}}{C_{v}}=\frac{\left(\frac{n}{2}+1\right) R}{\frac{n R}{2}}=\left(1+\frac{2}{n}\right) R\)
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