Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume V to V/2 (A isothermally and B adiabatically). The relation between pressure of the gas A ( PA) and pressure of gas B ( PB) is (a) PA PB (c) PA = PB (d) PA = 2PB

Answer: (a). VPV/2VA: isothermalB: adiabatic Isothermal: PA = P·2 = 2P. Adiabatic: PB = P·2γ, and γ > 1 so 2γ > 2. The adiabatic curve is steeper, so it reaches a higher pressure for the same compression. So the answer is (a) PA < PB.

Two samples A and B of gas initially at the same pressure and… | MHT CET 2026 (11 Apr, Shift 1)

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Thermodynamic Processes

Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume $V$ to $\frac{V}{2}$ (A isothermally and B adiabatically). The relation between pressure of the gas A ( $P_A$ ) and pressure of gas B ( $P_B$ ) is

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Answer: (a)

Isothermal: $P_A = P\cdot2 = 2P$ .
Adiabatic: $P_B = P\cdot2^{\gamma}$ , and $\gamma > 1$ so $2^{\gamma} > 2$ .
The adiabatic curve is steeper, so it reaches a higher pressure for the same compression.
So the answer is (a) $P_A < P_B$ .

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