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Two samples compressed from V to V/2, one isothermally and one adiabatically: compare final pressures

The same question, asked 2 times: 3 May 2023 S1, 11 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S1

    20
    There are two samples A and B of a certain gas, initially at the same temperature and pressure. Both are compressed from volume VV to V2\frac{V}{2}. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of A is

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  2. Question 2

    11 Apr 2026 S1

    116
    Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume VV to V2\dfrac{V}{2} (A isothermally and B adiabatically). The relation between pressure of the gas A (PA)(P_A) and pressure of gas B (PB)(P_B) is

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