A monoatomic ideal gas with γ = 5/3 is stored in a thermally insulated container and is suddenly compressed to 1/8 of its initial volume. The ratio Pf/Pi is:
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Question

A monoatomic ideal gas with γ = 5/3 is stored in a thermally insulated container and is suddenly compressed to 1/8 of its initial volume. The ratio Pf/Pi is:

G1 Physics · Accepted Answer

For an adiabatic process, PVᵞ = constant. Thus, PiViᵞ = PfVfᵞ. Therefore, Pf/Pi = (Vi/Vf)ᵞ. Given Vf = Vi/8 and γ = 5/3, Pf/Pi = 8⁵⁄³ = (2³)⁵⁄³ = 2⁵ = 32. Correct option: C.