Question 669: Thermodynamics & KTG

Question

A polyatomic gas is compressed to $\left(\frac{1}{8}ight)^{	ext {th }}$ of its volume adiabatically. If its initial pressure is $\mathrm{P}_0$, its new pressure will be [Given, $\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3}$ ]

Accepted Answer

A polyatomic gas undergoes adiabatic compression.
Final volume = $\dfrac{1}{8}$ of initial volume.
Pressure relation for adiabatic process:
$ P V^\gamma = 	ext{constant}, \quad \gamma = \frac{C_p}{C_v} = \frac{4}{3}. $
Step 1. Set up equation
$ P_0 V_0^\gamma = P V^\gamma $
where final volume $V = \frac{V_0}{8}$.
So,
$ P = P_0 \left( \frac{V_0}{V} ight)^\gamma. $
Step 2. Substitute values
$ \frac{V_0}{V} = \frac{V_0}{V_0/8} = 8. $
So,
$ P = P_0 \cdot 8^{\gamma}. $
$ \gamma = 	frac{4}{3}. $
Thus,
$ P = P_0 \cdot 8^{4/3}. $
Step 3. Simplify
$ 8^{4/3} = \big(8^{1/3}\big)^4 = 2^4 = 16. $
So,
$ P = 16 P_0. $
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Final Answer:
$ \boxed{16 P_0 \quad 	ext{(Option D)}} $

Answer

$\quad 6 \mathrm{P}_0$

Answer

$\quad 2 \mathrm{P}_0$

Answer

$\quad 8 \mathrm{P}_0$

Answer

$16 \mathrm{P}_0$

Thermodynamics & KTG

A polyatomic gas is compressed to \left(\frac{1}{8}\right)^{\text {th }} of its volume adiabatically. If its initial pressure is \mathrm{P}_0, its new pressure will be [Given, \frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\frac{4}{3} ]

Choose the correct answer: