CBEN 509 – Homework #1 – Due Friday 9/12/2025
1. (20 points/1 point each) Mark TRUE or FALSE for each of the following statements.
(a) An intensive property is independent of system size.
(b) A steady state entropy balance on a Joule-Thompson expansion results in a process with a negative
entropy generation.
(c) For a one-component system at equilibrium, the temperature and pressure are equal in each phase.
(d) One can use the NIST WebBook to obtain activity coefficients.
(e) The compression of a gas in an adiabatic and reversible compressor results in a gain of entropy.
(f) The compressibility of a vapor is always less than that of a liquid.
(g) The change in Gibbs free energy at the phase transition between a vapor and liquid is zero.
(h) If a gas is expanded through an isentropic and adiabatic turbine, the enthalpy of the exiting stream
is greater than the enthalpy of the inlet stream.
(i) Henry's law constant for oxygen in water can be used to calculate the concentration of oxygen in
blood.
(j) A two-phase ternary system has two degrees of freedom.
(k) A vapor mixture at 2.5 bar and 400 K can be treated as an ideal gas mixture.
(l) The enthalpy of fusion is the change in enthalpy in going from a liquid to a vapor.
(m) The partial molar enthalpy is a pure component property.
(n) The activity coefficient is a measure of liquid phase non-ideality.
(o) The Peng-Robinson equation of state is the only model used to obtain vapor fugacities.
(p) A steady-state energy balance on a Joule-Thompson expansion results in an isentropic process.
(q) The vapor fugacity coefficient of component i is zero at ideal gas conditions.
(r) The activity coefficient for an ideal solution is zero.
(s) The fugacity of component i in a mixture only depends on the temperature and pressure.
(t) A reference state is always at room temperature and atmospheric pressure.
2. (20 points) For each of the following situations, identify (i) the system, (ii) the boundaries, (iii) the
surroundings, and (iv) the kinds of interactions that can occur. DO NOT solve the problem.
a) Hot coffee is placed in a vacuum bottle and the top is sealed. Estimate the temperature of the coffee
after 4 hours.
b) A can of your favorite beverage, initially at room temperature, is placed in a freezer. How long
must the can remain there to cool to 40 oF?
c) Each tire on a car is charged with air to 0.20 MPa. The car is then driven for 300 m at an average
speed of 100 km/h. Estimate the tire pressure at the end of the trip.
d) Bill the untutored put his birthday balloon near a sunny window and, for the next few days,
observed interesting behavior: each afternoon the balloon was closer to the ceiling than it was in the
morning, and each day its maximum height was less than the day before. What was the maximum
temperature of the balloon each day, and how many days passed before the balloon failed to rise
from the floor?
3. In the design of a chemical process, you are asked to evaluate the performance of a turbine that
expands high pressure steam at 200 bar to saturated steam (90% quality) at 100 oC.
(a) (30 points) What is the temperature of the high pressure steam coming into the turbine if it
operates adiabatically and reversible? What is the amount of work (per kilogram of steam) from
this process? [Ans.: T ~ 955 K, work = -1312 kJ/kg]
(b) (30 points) What is the temperature of the high pressure steam coming into the turbine if it
operates at 80% efficiency to produce saturated vapor (90% quality) at 100 oC? What is the
amount of work (per kilogram of steam) for this process?
[Ans.: T ~ 860K, work = -1049.6 kJ/kg]