Question 883: Thermodynamics & KTG

Question

A gas at N.T.P. is suddenly compressed to $$\left(\frac{1}{4}ight)^{	ext {th }}$$ of its original volume. The final pressure in (Given $$\gamma=$$ ratio of sp. heats $$=\frac{3}{2}$$ ) atmosphere is ( $$\mathrm{P}=$$ original pressure)

Accepted Answer

In Adiabatic compression,
$$\mathrm{PV}^\gamma=$$ constant
Given $$V_{	ext {new }}=\frac{1}{4} V$$ and $$\gamma=\frac{3}{2}$$
$$\begin{array}{ll}
	herefore & \frac{\mathrm{P}_{	ext {new }}}{\mathrm{P}}=\left(\frac{\mathrm{V}}{\mathrm{V}_{	ext {new }}}ight)^\gamma=\left(\frac{\mathrm{V}}{\frac{1}{4} \mathrm{~V}}ight)^{3 / 2} \
	herefore & \mathrm{P}_{	ext {new }}=8 \mathrm{P}
\end{array}$$

Answer

$$4 \mathrm{P}$$

Answer

$$\frac{3}{2} \mathrm{P}$$

Answer

$$8 \mathrm{P}$$

Answer

$$\frac{1}{4} \mathrm{P}$$

Thermodynamics & KTG

A gas at N.T.P. is suddenly compressed to $\left(\frac{1}{4}\right)^{\text {th }} of its original volume. The final pressure in (Given \gamma= ratio of sp. heats =\frac{3}{2} ) atmosphere is ( \mathrm{P}=$ original pressure)

Choose the correct answer: