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The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when it is suddenly compressed to volume (V₀)/4 will be (given that γ is the ratio of the specific heats at constant pressure and at constant volume)

Asked in JEE Main 13th April 2nd Shift 2023 · Adiabatic Relations

• (1) P₀
• (2) P₀ 4^γ
• (3) P₀ 4^1/γ
• (4) 4P₀

Step-by-step solution

Why the other options are wrong

• (1) comes from would need γ=0
• (3) comes from inverts the exponent, which is what TV^γ-1 would give if misapplied
• (4) comes from is the isothermal answer, γ=1

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