An ideal gas undergoes a process in which T = T 0 + a V 3 , where T 0 and a are positive constants and V is the molar volume. The minimum pressure attainable is:

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An ideal gas undergoes a process in which T = T 0 ​ + a V 3 , where T 0 ​ and a are positive constants and V is the molar volume. The minimum pressure attainable is:

TestHub · Accepted Answer

P = V RT ​ = R ( V T 0 ​ ​ + a V 2 ) . Setting d V d P ​ = 0 gives − V 2 T 0 ​ ​ + 2 aV = 0 , so V 3 = 2 a T 0 ​ ​ . A. At V 3 = 2 a T 0 ​ ​ : P = R ( T 0 ​ V − 1 + a V 2 ) = R a 3 1 ​ T 0 3 2 ​ ​ ( 2 3 1 ​ + 2 − 3 2 ​ ) = 3 ⋅ 2 − 3 2 ​ R a 3 1 ​ T 0 3 2 ​ ​ , and 3 ⋅ 2 − 3 2 ​ = 2 3 ​ ⋅ 2 3 1 ​ . D.

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