Modern Engineering Thermodynamics

Problems 401
20.* Estimate h fg for water at 10.0°C using Eq. (11.17) and compare
your answer with the steam table value.
21.* Estimate v fg for water at 10.0°C using Eq. (11.17) and compare
your answer with the steam table value.
22.* Using the triple point of water (0.0100°C, 611.3 Pa) as a reference
state, estimate the saturation pressure of ice in equilibrium with
water vapor at −20.0°C ifh ig = 2834.8 kJ/kg is a constant over this
range.
23.* If saturated solid ice at –10.0°C is subjected to an isothermal
compression process to 200. MPa, will it melt? Use the triple
point (0.0100°C, 611.3 Pa) as the reference state, where h if =
−333.41 kJ/kg and v if = 9.08 × 10 –5 m 3 /kg. Sketch this process on
a p-T diagram.
24. At very low pressures, a substance has a saturation curve given
by p sat = exp(A 1 – A 2 /T sat ), where A 1 and A 2 are constants. Show
that h fg is constant for this substance.
25. At very low pressures, the saturation curve for a particular
substance is given by p sat = exp[A 1 + A 2 /T sat + A 3 (ln T sat )], where
A 1 , A 2 , and A 3 are constants. Show that h fg varies linearly with
T sat for this substance.
26. Using Eq. (11.22),
a. Show that the Joule-Thomson coefficient defined by
Eq. (6.25) can be written as
h
i
μ J = ð∂T/∂pÞ h
= Tð∂v/∂TÞ p
− v /c p
b. Use this result to evaluate the Joule-Thomson coefficient for
an ideal gas.
27. Assuming s = s(T, p) for a simple substance, derive Eqs. (11.26)
and (11.27) of this chapter.
28. The following equation of state has been proposed for a gas
pv = RT + A/T − B/T 2
where A and B are constants. Beginning with this equation,
develop equations based on the measurable properties p, v, andT
for the property changes u – u o , h – h o ,ands – s o ,whereu o , h o ,and
s o are reference state properties at p o , v o ,andT o .
29. Develop an equation based on measurable properties p, v, and
T for the property changes u 2 – u 1 , h 2 – h 1 , and s 2 – s l of a van
der Waals gas with constant specific heats. The van der Waals
equation of state, Eq. (3.44), can be written as p = RT/(v – b) –
a/v 2 , where a and b are constants.
30. Develop equations based on measurable properties p, v, and T
for the isothermal property changes (u 2 – u 1 ) T ,(h 2 – h 1 ) T , and
(s 2 – s 1 ) T of a Dieterici gas (see Eq. (3.45)).
31. Develop equations based on measurable properties p, v, and T
for the isothermal property changes (u 2 – u 1 ) T ,(h 2 – h 1 ) T , and
(s 2 – s 1 ) T of a Beattie-Bridgeman gas (see Eq. (3.47)).
32. Develop equations based on measurable properties p, v, and T
for the isothermal property changes (u 2 – u 1 ) T ,(h 2 – h 1 ) T , and
(s 2 – s 1 ) T of a Redlich-Kwong gas (see Eq. (3.48)).
33. Determine (∂c v /∂v) T for a Redlich-Kwong gas (see Eq. (3.48))
and integrate this to find the function c v = c v (T, v, v o ), where v 0
is a reference state specific volume.
34.* Using Eq. (11.30), calculate the difference between c p and c v for
(a) copper at 300°C, (b) mercury at 20°C, (c) glycerin at 20°C.
Use Tables 3.1 and 3.2 for compressibility values. The densities
at 20°C are ρ Cu = 8954 kg/m 3 , ρ Hg = 13,579 kg/m 3 , and ρ glyc =
1264 kg/m 3 .
35. Determine (∂c v /∂v) T for a van der Waals gas (see Eq. (3.44)).
36. Determine (∂c v /∂v) T for a Beattie-Bridgeman gas (see Eq. (3.47))
and integrate this to find the function c v = c v (T, v, v o ), where v o
is a reference state specific volume.
37. Saturated mercury vapor has an equation of state of the form
p sat =
RT
v
sat
− T v 2
sat
expðA 1 + A 2 /T sat + A 3 ln T sat Þ
where A 1 , A 2 , and A 3 are constants. The constant volume
specific heat c v is also constant for this material. Determine
equations that allow u g ,h g , and s g to be calculated relative to a
reference state at p o , v o , u o , and s o in terms of the measurable
quantities p, v, and T.
38.* A standard spark ignition piston-cylinder automobile engine
has a compression ratio of 8.60 to 1, and the intake air is at
0.100 MPa, 17.0°C. For an isentropic compression process, use
the gas tables (Table C.16b) to determine
a. The work required per unit mass of air compressed.
b. The temperature at the end of the compression stroke.
c. The pressure at the end of the compression stroke.
39. Air enters an isentropic, steady flow, axial compressor at
14.7 psia and 60.0°F and exits at 197 psia. Determine the
exhaust temperature and the input power per unit mass flow
rate. Use Table C.16a in Thermodynamic Tables to accompany
Modern Engineering Thermodynamics in your solution.
40.* An engineer claims to have designed an uninsulated diffuser that
expands 3.00 kg/s of air from 1.00 MPa, 37.0°C to 0.100 MPa,
17.0°C. The inlet and exit air velocities are 80.0 and 5.00 m/s,
respectively. Use the gas tables (Table C.16b) to determine the
heat transfer rate and entropy production rate for the diffuser, if
the average wall temperature is 27.0°C. Will the diffuser work as
designed?
41.* Determine the final pressure, temperature, and required work
per unit mass when 1.00 m 3 of air is isentropically compressed
from 0.150 MPa, 300. K to 0.100 m 3 using
a. Constant specific heat ideal gas equations.
b. The gas tables for air (Table C.16b).
42.* An insulated axial flow air compressor for a gas turbine engine
is being tested in a laboratory. The inlet conditions are 0.090
MPa and −3.00°C, and the outlet is at 0.286 MPa and 217°C.
Use the gas tables to determine the ratio of the power input for
an isentropic process to the actual adiabatic power input. This
ratio is defined to be the compressor’s isentropic efficiency.
43.* An insulated air compressor with an isentropic efficiency of
78.0% compresses air from 0.100 MPa, 290. K to 10.0 MPa. Use
the gas tables to determine the power required per unit mass
flow rate and the exit air temperature.
44. Use the gas tables (Table C.16a) to determine the final
temperature and the minimum possible power required to
compress 3.00 lbm/s of air from 14.7 psia, 40.0°F to10.0atm.in
a steady flow, adiabatic process.
45.* Air is compressed in an adiabatic, steady flow process from
0.081 MPa, 400. K, to 2.50 MPa with an isentropic efficiency of
85.0%. Use the gas tables to determine
a. The power required per unit mass flow rate.
b. The actual inlet temperature.
c. The entropy production rate per unit mass flow rate.
46.* An uninsulated piston-type air compressor operates in a steady
flow process from 0.100 MPa, 300. K to 2.00 MPa, 540. K. Use
the gas tables to determine per unit mass flow rate,
a. The power required.
b. The heat transfer rate.