Modern Engineering Thermodynamics

Problems 93
c. For a saturated mixture of liquid and vapor, explain whether
or not the pressure and temperature can be varied
independently.
23. A vessel with a volume of 10.0 ft 3 contains 3.00 lbm of a
mixture of liquid water and water vapor in equilibrium at a
pressure of 100. psia (Figure 3.28). Determine
a. The mass of liquid present.
b. The mass of vapor present.
c. Hydrogen gas is heated at a constant pressure of 0.00 psia
from 0 to 5000.°F.
d. Air is compressed from 0.00°F, 0.00 psia to 1000.°F, 5000.
psia.
34. Determine the changes in specific internal energy and specific
enthalpy as air is compressed from 0.00°F, 14.7 psia to 1000.°F,
5000. psia (Figure 3.29). Assume variable specific heat ideal gas
behavior.
p = 100. psia
Total volume = 10.0 ft 3
FIGURE 3.28
Problem 23.
Vapor
Liquid
Total mass of
liquid + vapor = 3.00 lbm
24.* Determine the change in the specific internal energy of 3.00 kg
of graphite as it is heated at atmospheric pressure from 20.0 to
200.°C. Assume a constant specific heat.
25. Determine the change in the enthalpy of 5.00 lbm of ice as it is
heated from 22.0 to 32.0°F under constant atmospheric
pressure. Assume a constant specific heat.
26.* Determine the change in the specific internal energy of solid
aluminum as it is heated at atmospheric pressure from 300. to
500. K. Use an average specific heat over this temperature range.
27. Determine the change in the specific enthalpy of solid lead as it
is heated from 14.7 psia, 80.0°F to 1000. psia, 200.°F. The
density of lead is 710. lbm/ft 3 . Assume a constant specific heat.
28. Determine the change in the specific internal energy of 7.00 lbm
of methane gas as it is heated from 32.0 to 200.°F at
atmospheric pressure. Assume ideal gas behavior.
29.* Determine the change in the specific enthalpy of carbon dioxide
gas as it is heated at a constant pressure of 1 atm from 300. to
500. K. Assume ideal gas behavior.
30.* Argon gas is heated in a constant pressure process from 20.0 to
500.°C. Assuming ideal gas behavior, determine
a. The ratio of the final to initial volumes.
b. The change in specific internal energy.
c. The change in specific enthalpy of the argon.
31. Helium gas is heated in a constant volume process from −200.
to 500.°F. Assuming ideal gas behavior, determine
a. The ratio of the final to initial pressures.
b. The change in specific internal energy.
c. The change in specific enthalpy of the helium.
32. Gaseous oxygen is heated in a constant temperature process
until its volume is doubled. Assuming ideal gas behavior,
determine
a. The ratio of the final to initial pressures.
b. The change in specific internal energy.
c. The change in specific enthalpy of the oxygen.
33. Using Figure 3.21, estimate the average values for the constant
pressure and constant volume specific heats for the following
gases and processes:
a. Carbon dioxide is heated at a constant pressure of 10,000 psia
from 1000. to 2000.°F.
b. Carbon dioxide gas is compressed isothermally at 1000.°F
from 0 to 10,000. psia.
FIGURE 3.29
Problem 34.
T 1 = 0.00°F
p 1 = 14.7 psia
u 2 − u 1 = ?
h 2 − h 1 = ?
T 2 = 1000. °F
p 2 = 5000. psia
State 1 State 2
35. Professor John L. Krohn at Arkansas Tech University invented a
process whereby air is heated at constant volume from 60.0°F
and v = 3.30 ft 3 /lbm to a pressure of 180. psi. The air then
expands adiabatically to atmospheric pressure and v = 14.6 ft 3 /
lbm. Assuming ideal gas behavior with variable specific heat,
determine
a. The temperature of the heated air (T 2 )in°F.
b. The heat transfer for the first process in Btu/lbm.
c. The work for the second process in Btu/lbm,
36. Professor Krohn uses the constant pressure specific heat
equation for water vapor given in by c p = A(B + CT + DT 2 +
ET 3 + FT 4 ), where A = 0.1102 Btu/lbm · R, B = 4.070,
C = −0.000616 R −1 , D = 1.281 × 10 −6 R −2 , E = −0.508 × 10 −9
R −3 , F = 0.0769 × 10 −12 R −4 , and T is in Rankine (R). He wants
you to estimate the change in enthalpy for water vapor from
p 1 = 14.7 psi, T 1 = 250.°F top 2 = 14.7 psi, T 2 = 500.°F, and
compare this result to the change in enthalpy found in the
superheated steam tables.
37.* In 1879, the French physicist Emile Amagat generated
experimental data in a mine shaft at Verpilleux, France, for his
research on the compressibility of gases. There, he used a vertical
column of mercury 327 m high to measure the compressibility
of nitrogen at a pressure of 430. atm. Assuming the temperature
at the bottom of the mine shaft was 30.0°C, determine the
specific volume of the nitrogen, assuming it is an ideal gas with
constant specific heats.
38.* Calculate the specific volume of hydrogen (H 2 ) gas at a
temperature of 20.0°C and a pressure of 11.0 MPa using
a. The ideal gas equation of state.
b. The Clausius equation of state (use the van der Waals value
for b).
39. Determine the temperature of water vapor at 200. psia when it
has a specific volume of 2.724 ft 3 /lbm using
a. The ideal gas equation of state.
b. The van der Waals equation of state.
c. The steam tables (Table C.3a).
Then compute the percentage error of a and b with the actual
value given in c.