JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Heat & Thermodynamics

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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 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:

(A)8
(B) $8^{\frac{3}{2}}$
(C) $\frac{1}{8}$
(D)4✓ Correct

Answer: (D)

Solution

For the isothermal change in A,

P V = const

gives

P_{A} = P \times 8 = 8 P

. For the adiabatic change in B,

P V^{γ} = const

with

γ = \frac{5}{3}

for a monoatomic gas gives

P_{B} = P \times 8^{5/3} = P \times 2^{5} = 32 P

. The ratio is

\frac{P _{B}}{P _{A}} = \frac{32 P}{8 P} = 4

JEE Main · 2023 · 10 Apr 2023 · Shift 1 · Single correct option

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