The ratio of specific heats $\left(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\right)$ in terms of degree of freedom (f) is given by:

(B) $\left(1+\frac{2}{\mathrm{f}}\right)$

(A) $\left(1+\frac{\mathrm{f}}{3}\right)$

(C) $\left(1+\frac{f}{2}\right)$

(D) $\left(1+\frac{1}{\mathrm{f}}\right)$

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Heat & Thermodynamics

The ratio of specific heats

(\frac{C _{P}}{C _{V}})

in terms of degree of freedom (f) is given by:

(A) $(1 + \frac{f}{3})$
(B) $(1 + \frac{2}{f})$ ✓ Correct
(C) $(1 + \frac{f}{2})$
(D) $(1 + \frac{1}{f})$

Answer: (B)

Solution

For an ideal gas,

C_{V} = \frac{f R}{2}

and

C_{P} = C_{V} + R = \frac{f R}{2} + R = \frac{( f + 2 ) R}{2}

. Therefore,

γ = \frac{C _{P}}{C _{V}} = \frac{f + 2}{f} = 1 + \frac{2}{f}

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Single correct option

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