An ideal gas initially has pressure P₀ and volume V₀. It is suddenly compressed to volume V₀/4. If γ is the ratio of specific heats, the final pressure is:
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Question

An ideal gas initially has pressure P₀ and volume V₀. It is suddenly compressed to volume V₀/4. If γ is the ratio of specific heats, the final pressure is:

G1 Physics · Accepted Answer

Sudden compression is treated as an adiabatic process. For an adiabatic process: PVᵞ = constant Thus, P₀V₀ᵞ = P₂(V₀/4)ᵞ Therefore, P₂ = P₀ [V₀/(V₀/4)]ᵞ = P₀·4ᵞ Hence option D follows.