1. How many phase rule variables must be specified to fix the
thermodynamic state of each of the following systems?
(a) A sealed flask containing a liquid ethanol-water mixture in
equilibrium with its vapor.
(b) A sealed flask containing a liquid ethanol-water mixture in
equilibrium with its vapor and nitrogen.
(c) A sealed flask containing ethanol, toluene, and water as two
liquid phases plus vapor.
2. A closed, nonreactive system contains species 1 and 2 in
vapor/liquid equilibrium. Species 2 is a very light gas, essentially
insoluble in the liquid phase. The vapor phase contains both species
1 and 2. Some additional moles of species 2 are added to the
system, which is then restored to its initial T and P. As a result of
the process, does the total number of moles of liquid increase,
decrease, or remain unchanged?
3. A cylinder contains 0.7 kg of steam at the temperature of 100 °C
trapped below a piston. The piston is 1.1. kg, and its area is 10 cm².
The pressure above the piston is 100 kPa. The steam is heated to
104 °C. Assuming that the value of Cp for steam remains 1.89
kJ/(kg K) during the temperature range, solve the following
problems. Assume g = 9.8 m/s².
(a) Find the total heat, work, and internal energy change of steam
when the piston is slowly elevated by a height of 25 cm (assume
constant pressure inside the piston).
(b) Find the total internal energy change of steam when the piston
is held in place by latches (i.e., constant volume).
4. 2 kg of air is heated reversibly from an initial state of 325 K and 1
atm. Calculate W, Q, and U for the following cases. Assume for air
that PV/T = 83.14 (bar cm³)/(mol K) and Cp = 29 J/(mol K).
(a) At constant pressure until volume doubles.
(b) At constant volume until pressure triples.
5. The heat engine produces power of 100,000 kW. It operates
between heat reservoirs at 800 K and cold reservoirs at 225 K with
a thermal efficiency of. Determine the rates at which heat is
absorbed from the hot reservoir and discarded to the cold reservoir.
6. 1.5 kg/s of cool water at 298 K and 1.0 kg/s of hot water at 340 K
are mixed to produce warm water at a steady state. Heat is lost to
the surrounding during the mixing at a rate of 40 kJ/s. What is the
temperature of the warm water? Assume the specific heat of water
(i.e., heat capacity) is 4.18 kJ/(kg K) and the kinetic energy,
potential energy, and shaft work are negligible.
