CHEE 220
Intro to Thermodynamic Processes
Homework #5
Due Date: February 16 (Friday)
Spring 2024
Individual Assignment
1. You have used the Unit Operations worksheet and completed the items below for various unit operations.
However, one unit operation that was covered in the textbook AND the videos, but not covered in the class
sessions was the nozzle. To that end, perform the same analysis that was done on the worksheet, but this time
for the nozzle.
Constant
Unit
Purpose
Entering
Phase
Exiting
Phase
T
(Y/N)?
P
(Y/N)?
Typically
model as
Adiabatic
(Y/N)?
Reduced 1st Law
Expression
(time-dep. balance)
Nozzle
2. Superheated steam enters a horizontal nozzle that has an inlet diameter that measures 2.5 cm and an outlet
diameter that measures 1 cm. Its outlet velocity has been measured at 30 m/s. The steam that enters the
nozzle is at 650 ˚C and 1350 kPa and the steam that exits the nozzle is at 400 ˚C and 100 kPa.
a. Determine the velocity of the steam upon entering the nozzle. Hint: the mass flow rate into and out of the
nozzle will be the same – it is at steady state. This part of the problem requires you to calculate the velocity
from mass flow rate (like a problem from the last homework assignment).
b. Your reduced 1st Law expression (from question 1) is the typical expression in these type of problems.
However, despite how much you might insulate the nozzle, you will still have some heat losses. To that end,
please calculate the rate of heat loss through the nozzle. Note: you have enough information to calculate
the kinetic energy changes (from the problem statement and your work in part a), so please include those as
well.
3. In a similar way to question 1 above, while we have discussed heat capacity in this course, we haven’t discussed
in the classroom sessions about the difference between the liquid and vapor heat capacity for a given substance.
Of course, the textbook covers that (and the videos).
To that end… for a project you needed to find the heat capacity of methyl ethyl ketone as a liquid and vapor.
You wrote down two values: 158.4 J/mol-K and 101.7 J/mol-K. However, when you went to use those numbers
a few days later, you did not label which was the liquid and which was the vapor. You forgot – it happens.
However, which one do you think is the liquid value and why?
4. (old exam problem) You work as an engineer for a company looking to use a different substance than H2O in a
Rankine Cycle. Your job is to analyze the boiler. You are not told the name of the substance (it is proprietary),
but you are given a variety of thermophysical properties. You are interested in determining the heat load on the
boiler. However, in this problem you are ONLY concerned with the thermodynamic path and will NOT calculate
any values (though you need to put the right values into the formulas…you just won’t make a calculation).
Property
Tb (C)
Value
29.0
Hvap
(kJ/mol)
20.0
Vliq
Tc (C)
(cm3/mol)
50.1
191.0
Pc (bar)
41.1
CpLiq
(J/mol-K)
66.8
Cpvap
(J/mol-K)
24.2
MW
92.0
You assume that a compressed liquid arrives at the boiler at 29.0 C and 10 bar. It leaves the boiler as a
superheated vapor at 100.0 C. As usual, the boiler operates in an isobaric manner.
(a) Write down the appropriate energy balance for this system. Note: Unlike the previous two problems, you
do NOT have to start at the appropriate/general balance and cross out terms. Here…just write down the
energy balance you will use.
(b) Provide a suitable thermodynamic path to obtain the desired state value change (i.e. based on your answer
to part (a)) and describe (via an equation or directly the value, if applicable) how you would calculate each
step. Make/describe appropriate assumptions, where applicable.
(c) For each step in part b, calculate the value required in units of kJ/mol.
5. (old exam problem) Provide the proper number/quantity below for each:
i. Value of Z (compressibility factor) for the ideal gas:
ii. Value of the square-well epsilon parameter if the system is modeled as an ideal gas:
iii. The heat of vaporization of water at its critical point:
iv. The value of the system volume that best validates the ideal gas assumption: