Equations of State Questions and Answers

Answer: C

Both are true and the reason gives the criterion: mechanical stability requires the isothermal compressibility to be positive, and the middle branch violates it everywhere. The Maxwell construction replaces that branch with a straight line.

Answer: D

The construction operates on the loop an equation of state produces, so it presupposes one rather than replacing it. The other three describe exactly what it does. It is the standard way of extracting a saturation pressure.

Answer: A

There is only one fluid phase above the critical temperature, so only one physically meaningful volume can exist at a given pressure. The mathematics reflects the physics directly. Below the critical temperature the extra roots reappear.

Answer: B

An equation of state has a single a and b, so a mixture requires a rule for combining the pure values. The classical rules are quadratic in composition for a and linear for b. Cross terms then need a binary interaction parameter.

Answer: C

The geometric mean rule for the cross term is only approximate, and the small correction parameter is regressed from binary equilibrium measurements. Its value is often near zero for similar molecules and significant for dissimilar ones.

Answer: D

Four tenths of five hundredths plus six tenths of one tenth gives eight hundredths. Taking a plain arithmetic average instead of a mole fraction weighting is the common error and gives seventy-five thousandths instead.

Answer: A

The sequence runs from eighteen seventy-three through the mid twentieth century to nineteen seventy-six, and each was a response to a shortcoming of the one before. The order is also the order of increasing accuracy for phase equilibrium.

Answer: B

Correct answer: the gas is at moderate pressure with known coefficients

The virial equation is a theoretically grounded series in density, and truncating it after the second coefficient describes a gas well up to moderate pressures - roughly to half the critical density. What it cannot do is represent a liquid or the critical region, since the truncated series has no second root; a cubic equation is used there. Its virtue is that the coefficients have real meaning, and its limitation is that they must be known.

Answer: C

The virial equation is a power series rather than a cubic in volume, and it cannot produce the three roots that give a liquid and a vapour. The grouping matters because only the cubics can be used for flash calculations.

Answer: D

Both are true and the reason gives the trade-off: a flash calculation may be repeated millions of times in a simulation, so an equation that solves in microseconds and is right to a few per cent beats a more exact but costly alternative.