Consider two containers A and B containing monoatomic gases at the same Pressure $$P$$, Volume $$V$$ and Temperature $$T$$. The gas in A is compressed isothermally to $$\frac{1}{8}$$ of its original volume while the gas in B is compressed adiabatically to $$\frac{1}{8}$$ of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Given: Both gases start at pressure P, volume V. Monoatomic gas ($$\gamma = 5/3$$).

Container A (isothermal compression):

$$P_A V_A = PV$$, with $$V_A = V/8$$:

$$P_A = 8P$$

Container B (adiabatic compression):

$$P_B V_B^\gamma = PV^\gamma$$, with $$V_B = V/8$$:

$$P_B (V/8)^{5/3} = PV^{5/3}$$

$$P_B = P \times 8^{5/3} = P \times (2^3)^{5/3} = P \times 2^5 = 32P$$

Ratio:

$$\frac{P_B}{P_A} = \frac{32P}{8P} = 4$$

The correct answer is Option 2: 4.