An ideal gas (γ = 1.4), originally at 300 K and 100 kPa, is compressed adiabatically in a single step against a constant external pressure until its temperature reaches 600 K. What is the minimum exte

Question

An ideal gas (γ = 1.4), originally at 300 K and 100 kPa, is compressed adiabatically in a single step against a constant external pressure until its temperature reaches 600 K. What is the minimum external pressure that must be applied?

TestHub · Accepted Answer

q = 0, so nC v (T 2 - T 1 ) = -P ext (V 2 - V 1 ) with C v = 5/2R and the final pressure equal to P ext . With V 2 = nRT 2 /P ext and V 1 = nRT 1 /P 1 : 5/2(300) = (P ext )/P 1 (300) - 600, so (P ext )/P 1 = 1350/300 = 4.5, giving 450 kPa. (A reversible adiabatic path would end at 100 × 2 3.5 = 1131 kPa, which is the distractor in option b.) Matches (a).

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