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Triple point

Ttp, ptp

lnf psat,L " _ Ahvap f1 TT°P 1 + vLpTP ( p j)

psat,s = psat,L

(5.23S), (5.23L)

References

1. 1. M. Potter and C. Somerton, Theory and Problems in Engineering Thermodynamics, McGraw-Hill (1993)

Problems for Chap. 5

5.1 In the notes, Eq(5.6) was integrated assuming that Ahvap = hg - hL is constant. More generally, Ahvap varies with temperature according to Eq (5.7).

(a) Using Eq (5.7) in the Clausius-Clapyron equation, show that lnpsat =A -B/T+DlnT

and identify A, B and D. (take the normal boiling point as the reference state).

(b) Assuming that the liquid and vapor are monatomic and CVL = 3R, where R is the gas constant, what is the value of the coefficient D?

(c) For water, use your best estimates of CPg and CPL to determine D.

5.2 The vapor pressures (in atm) of the liquid and solid phases of a particular metal are given by the equation:

where T is in K. The coefficients in this equation are:

Transition A B(K) D

solid-gas 19.25 15773 -0.755 liquid-gas 21.79 15246 -1.255

Using the results of Prob. 5.1a, identify the coefficients B and D. Then, calculate:

(a) The normal boiling point (i.e., the temperature at which psat = 1 atm).

(b) The triple point temperature.

(c) The heat of vaporization at the normal boiling point.)

(d) The difference between the heat capacities of the liquid and solid, CPL - CPs

(e). The heat of fusion at the triple point

(f) The slope of the liquid-solid boundary line at the triple point. The densities of the liquid and solid phases are 5.66 and 7.14 g/cm3 and the atomic weight of the metal is 65.4.

5.3 The vapor pressures of solid and liquid CO2 are expressed by:

The heat of fusion of CO2 is 8.3 kJ/mole and the triple point temperature is 217 K.

(a) Determine the numerical values of AL and BL.

(b) What is the stable condensed phase of CO2 at 1 atm pressure?

(c) At what temperature is the vapor pressure equal to 1 atm?

5.4 The triple point of water is defined as 0.01oC and 611 Pa. Show why the freezing point of water at 1 atm pressure is 0oC.

5.5 The steam tables A.1 and A.2 contain entries for vf, vg ,..sf, sg, but none for gf and gg.

(a) What would be the most important characteristic of gf and gg if they were displayed in the tables?

(b) How would gf and gg be determined from the entries in the existing pllltables?

5.6 The specific heat of solid copper(CP) is shown on the plot below. Other properties are:

atomic weight: 63.5 melting point: 1356 K

heat of sublimation: 329 kJ/mole (assume this to be independent of temperature) vapor pressure at the melting point: 0.0505 Pa

At 1200 K, determine the following properties of the saturated vapor:

(a) the saturation pressure

(b) the absolute entropy of the vapor. Use Cp = 2.48x10-7T3 cal/g-K from 0 - 30 K, and Cp = 0.085 + 2.7x10-5T cal/g-K from 300 K to the melting point. In the intermediate range, CP(T) must be obtained from the graph. Convert units to J/g-K.

Temperature, K

5.7 Using the triple-point data for water from Table A.5 of Chap. 2 and assuming the heat of sublimation of ice to be constant, estimate the water vapor pressure over ice at -40oC. Compare to the value given in Table A.5.

5.8 A compressed liquid at Ti and pi is heated at constant pressure by addition of a quantity q of heat per mole. In the final state, two phases are present at the temperature T2 fixed by the pressure. The vapor and liquid heat capacities are CPg and Cpl and the enthalpy of vaporization at T1 is AHV1.

Derive the equation for the fraction of liquid vaporized in this process by either the top (A-B) or bottom (D-E) two-step routes shown below:

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