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Adiabatic compression to a fraction of volume: final pressure or temperature

This type of question, asked 14 times: May 2022 S1, 16 May 2023 S1, 9 May 2024 S1, 9 May 2024 S2, 11 May 2024 S1, 12 May 2024 S1, 14 May 2024 S2, 20 Apr 2025 S1, 23 Apr 2025 S1, 25 Apr 2025 S1, 15 Apr 2026 S1, 16 Apr 2026 S1, 19 Apr 2026 S1, 20 Apr 2026 S1. All 14 questions below, oldest first.

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  1. Question 1

    May 2022 S1

    19
    A monoatomic gas (γ=53)\left(\gamma = \frac{5}{3}\right) initially at 27°C having volume VV is suddenly compressed to one-eighth of its original volume V8\frac{V}{8}. After the compression its temperature becomes

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  2. Question 2

    16 May 2023 S1

    50
    In ideal gas of 27°C27°C is compressed adiabatically to 827\frac{8}{27} of its original volume. If γ=53\gamma = \frac{5}{3}, the rise in temperature of a gas is

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  3. Question 3

    9 May 2024 S1

    21
    A gas at N.T.P. is suddenly compressed to 14\frac{1}{4}th of its original volume. The final pressure in atmosphere is (Given γ=\gamma= ratio of sp. heats =32=\frac{3}{2}) (P=P= original pressure)

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  4. Question 4

    9 May 2024 S2

    24
    A gas at N.T.P. is suddenly compressed to one-fourth of its original volume. If γ=1.5\gamma = 1.5, then the final pressure is

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  5. Question 5

    11 May 2024 S1

    39
    A diatomic gas γ=75\gamma = \frac{7}{5} is compressed adiabatically to volume Vi32\frac{V_i}{32} where ViV_i is its initial volume. The initial temperature of the gas is TiT_i in Kelvin and the final temperature is xTixT_i. The value of x is

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  6. Question 6

    12 May 2024 S1

    35
    A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If CpCv=γ=1.5\frac{C_{p}}{C_{v}}=\gamma=1.5, then the increase in its temperature is

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  7. Question 7

    14 May 2024 S2

    29
    The pressure and density of a diatomic gas (γ=75)\left(\gamma = \frac{7}{5}\right) changes adiabatically from (P,ρ)(P, \rho) to (P′,ρ′)(P', \rho'). If ρ′ρ=32\frac{\rho'}{\rho} = 32 then P′P\frac{P'}{P} should be

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  8. Question 8

    20 Apr 2025 S1

    30
    A diatomic gas (γ=75)\left( \gamma=\frac{7}{5} \right) is compressed adiabatically to volume V032\frac{V_{0}}{32}, where V0V_{0} is its initial volume. The initial temperature of the gas is TiT_{i} in kelvin and the final temperature is xTixT_{i} in kelvin. The value of xx is

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  9. Question 9

    23 Apr 2025 S1

    30
    A polyatomic gas is compressed to (18)th \left( \frac{1}{8} \right)^{\text{th~}} of its volume adiabatically. If its initial pressure is P0P_{0}, its new pressure will be [Given, CpCv=43\frac{C_{p}}{C_{v}}=\frac{4}{3} ]

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  10. Question 10

    25 Apr 2025 S1

    44
    A monoatomic ideal gas is compressed adiabatically to (127)\left( \frac{1}{27} \right) of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is

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  11. Question 11

    15 Apr 2026 S1

    116
    A monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to (18)th\left(\dfrac{1}{8}\right)^{th} of its initial volume. The ratio of final pressure to initial pressure is

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  12. Question 12

    16 Apr 2026 S1

    118
    An ideal gas at 27∘27^\circC is compressed adiabatically to (827)\left(\dfrac{8}{27}\right) of its original volume. If γ=5/3\gamma = 5/3, then the rise in temperature of a gas is

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  13. Question 13

    19 Apr 2026 S1

    115
    A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If γ=1.5\gamma = 1.5, then the increase in the temperature of the gas in Kelvin is (γ\gamma is the ratio of specific heats)

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  14. Question 14

    20 Apr 2026 S1

    114
    A rigid diatomic gas (γ=75)\left(\gamma = \dfrac{7}{5}\right) is compressed adiabatically to volume (Vi32)\left(\dfrac{V_i}{32}\right), where ViV_i is the initial volume. The initial temperature of the gas is 'TiT_i' K and the final temperature is 'xTixT_i' K. The value of xx is

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