Heat Capacity and Enthalpy Changes Questions and Answers

Answer: A

Correct answer: rate of change of enthalpy with temperature

\[ C_p = \left(\frac{\partial H}{\partial T}\right)_P. \] Its counterpart \( C_v \) is the rate of change of internal energy at constant volume, and the two differ by \( R \) for an ideal gas. Because most process work is done at constant pressure, \( C_p \) is the one tabulated and the one that appears in enthalpy balances.

Answer: B

It rises with temperature for most substances, which is why the tabulated correlations are polynomials. Treating it as constant is acceptable over a narrow range and misleading over a wide one. Polynomial coefficients are tabulated for this reason.

Answer: C

Correct answer: 3000 joules

\[ Q = nC_p\Delta T = 4 \times 30 \times 25 = 3000\ \mathrm{J}. \] All three factors are needed, and each of the distractors omits one: 120 leaves out the temperature rise, 750 the mole count and 300 the heat capacity. The temperature difference may be taken in kelvin or Celsius indifferently, since only the interval matters.

Answer: D

Both are true and the reason gives the definition: the mean is not a simple average of the end values but the value that gives the correct area, and it is tabulated against a reference temperature. Reading the interval off the table matters as much as the value.

Answer: A

The same substance has different mean capacities over different ranges, so a value without its interval cannot be used. Tables usually fix one end at a reference such as twenty-five degrees Celsius. Two mean values may be combined to cover another interval.

Answer: B

Correct answer: A-2, B-4, C-1, D-3

Four estimating rules for four different quantities. Kopp’s rule adds atomic contributions to estimate the heat capacity of a solid. Trouton’s rule puts the entropy of vaporisation at the normal boiling point near 88 joules per mole kelvin for ordinary liquids. Kirchhoff’s relation corrects a heat of reaction from one temperature to another using the heat capacity difference. And the Watson correlation scales a latent heat to another temperature using the reduced temperature.

Answer: C

Each element is assigned an atomic heat capacity and the compound value is the sum. The rule is crude but useful where nothing has been measured, which is often the case for minerals and solids. It works less well at low temperature.

Answer: D

The first two are correct. The third holds only when the mole fractions happen to be equal, and it is exactly the same weighting error that appears in computing an average molar mass. Mole fractions are the correct weighting throughout.

Answer: A

A quarter of forty plus three quarters of twenty gives ten plus fifteen. Taking the simple average of forty and twenty would give thirty and ignores the very different amounts present. The weighting must always follow the composition.

Answer: B

Correct answer: saturated water at the triple point

Steam tables set enthalpy and entropy to zero for saturated liquid water at the triple point, 0.01 degrees Celsius. The choice is arbitrary, as any enthalpy datum must be, and it is harmless because every calculation involves a difference in which the datum cancels - provided the same table, or the same datum, is used throughout.