A monoatomic gas at pressure P₁, having a volume V, expands isothermally to volume 2V and then adiabatically to volume 16V. The final pressure of the gas is (take γ = 5/3):
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A monoatomic gas at pressure P₁, having a volume V, expands isothermally to volume 2V and then adiabatically to volume 16V. The final pressure of the gas is (take γ = 5/3):

G1 Physics · Accepted Answer

Step 1: Isothermal stage, from volume V to 2V: PV = constant. Step 2: With initial pressure P₁, the pressure after this stage is P₂ = P₁V/(2V) = P₁/2. Step 3: Adiabatic stage, from 2V to 16V: PVᵞ = constant, with γ = 5/3. Step 4: Therefore P₃ = P₂[(2V)/(16V)]ᵞ = (P₁/2)(1/8)⁽⁵⁄³⁾. Step 5: Since 8 = 2³, (1/8)⁽⁵⁄³⁾ = 1/2⁵ = 1/32. Step 6: P₃ = (P₁/2)(1/32) = P₁/64. Final answer: (C) P₁/64.