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Monoatomic gas in a cylinder expands adiabatically when the piston is released: temperature ratio from column lengths

The same question, asked 4 times: 15 May 2023 S2*, 12 May 2024 S2*, 22 Apr 2025 S2*, 13 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S2

    17
    A monoatomic ideal gas, initially at temperature T1T_1 is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature T2T_2 by releasing the piston suddenly. L1L_1 and L2L_2 are the lengths of the gas columns before and after the expansion respectively. The ratio T2/T1T_2/T_1 is

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  2. Question 2

    12 May 2024 S2

    3
    A monoatomic ideal gas initially at temperature 'T1T_1' is enclosed in a cylinder fitted with massless frictionless piston. By releasing the piston suddenly the gas is allowed to expand adiabatically to a temperature 'T2T_2'. If 'L1L_1' and 'L2L_2' are the lengths [of the gas columns before and after expansion respectively, then T2T1\frac{T_2}{T_1} is]

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  3. Question 3

    22 Apr 2025 S2

    44
    A monoatomic ideal gas, initially at temperature T1T_{1} is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature T2T_{2}. If L1L_{1} and L2L_{2} are the lengths of the gas columns before and after expansion respectively, then (T2/T1)\left( T_{2}/T_{1} \right) is given by

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  4. Question 4

    13 May 2026 S2

    117
    A monoatomic ideal gas, initially at temperature T1T_1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2T_2 by releasing the piston suddenly. If L1L_1 and L2L_2 be the lengths of the gas column before and after expansion respectively, then T1T2\dfrac{T_1}{T_2} is

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