Problem 1.1: The density of liquid ammonia (NH3) at 0 °F, 31 psi, is 41.3 lb/ft3.
a) Calculate the specific volume in ft3/lb, cm3/g and m3/kg.
b) Calculate the molar volume in ft3/lbmol, cm3/mol and m3/mol.
Problem 1.2: The equation below gives the boiling temperature of isopropanol as a function of pressure:
where T is in kelvin, P is in bar, and the parameters A, B, and C are
A = 4.57795, B = 1221.423, C = −87.474
Obtain an equation that gives the boiling temperature in °F, as a function of ln P, with P in psi. Hint: The equation is of the form
but the constants A′, B′, and C′ have different values from those given above.
Problem 1.3: a) At 0.01 °C, 611.73 Pa, water coexists in three phases, liquid, solid (ice), and vapor. Calculate the mean thermal velocity () in each of the three phases in m/s, km/hr and miles per hour.
b) Calculate the mean translational kinetic energy contained in 1 kg of ice, 1 kg of liquid water, and 1 kg of water vapor at the triple point.
c) Calculate the mean translational kinetic energy of an oxygen molecule in air at 0.01 °C, 1 bar.
Problem 1.4: The intermolecular potential of methane is given by the following equation:
with a = 2.05482 × 10−21 J, σ = 3.786 Å, and r is the distance between molecules (in Å).
a) Make a plot of this potential in the range r = 3 Åto10 Å.
b) Calculate the distance r* (in Å) where the potential has a minimum.
c) Estimate the density of liquid methane based on this potential.
Find the density of liquid methane in a handbook and compare your answer to the tabulated value.
Problem 1.5: a) Estimate the mean distance between molecules in liquid water. Assume for simplicity that molecules sit on a regular square lattice.
b) Repeat for steam at 1 bar, 200 °C (density 4.6 × 10−4 g/cm3).
Report the results in Å.
Problem 1.6: In 1656, Otto von Guericke of Magdeburg presented his invention, a vacuum pump, through a demonstration that became a popular sensation. A metal sphere made of two hemispheres (now known as the Magdeburg hemispheres) was evacuated, so that a vacuum would hold the two pieces together. Von Guericke would then have several horses (by one account, 30 of them, in two teams of 15) pulling, unsuccessfully, to separate the hemispheres. The demonstration would end with the opening of a valve that removed the vacuum and allowed the hemispheres to separate. Suppose that the diameter of the sphere is 50 cm and the sphere is completely evacuated. The sphere is hung from the ceiling and you pull the other half with the force of your body weight. Will the hemispheres come apart? Support your answer with calculations.