Chapter 4: Temperature
Objectives:
1. Define what temperature is.
2. Explain the difference between absolute and relative temperature.
3. Know the reference points for the temperature scales.
4. Convert a temperature in any of the four common scales to any others.
5. Convert an expression involving units of temperature to other units of temperature.
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Temperature
Temperature is a measure of the energy (mostly kinetic) of the molecules in a system.
The most commonly used temperature scales are two based on a relative scale, degrees
Celsius (°C) and Fahrenheit (°F), and two based on an absolute temperature scale, degrees
Kelvin (K) and Rankine (°R).
Relative scales are based on a specified reference temperature (32 ̊F or 0 ̊C) that occurs in an
ice-water mixture (the freezing point of water).
Absolute scales are defined such that absolute zero has a value of 0 (lowest temperature
attainable in nature: -273.15°C and -459.67°F).
The size of the degree is the same as the Celsius degree (Kelvin scale)
or a Fahrenheit degree (Rankine scale).
Comparison of magnitudes of various
temperature units:
°
1 Δ ̊C
1ΔK
1 Δ ̊F
1 Δ°R
1.8 Δ ̊F
1 Δ ̊C
1.8 Δ°R
1 ΔK
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Temperature Conversion
Temperatures expressed in one of these scales may be converted to equivalent
temperatures in another scale by using the following relationships.
T (°K) = T (°C )× (1 ΔK/1Δ ̊C) + 273.15 K
T (°R) = T (°F ) ×(1 Δ°R/Δ ̊F ) + 459.67 °R
T (°R) = T (K ) ×(1.8Δ°R/ΔK)
T( ̊F) = T ( ̊C) ×(1.8Δ ̊F/Δ ̊C ) +32 ̊F
T (°K) = T (°C) + 273.15 K
T (°R) = T (°F ) + 459.67 °R
T (°R) = T (K ) ×1.8
T( ̊F) = T ( ̊C) ×1.8 +32 ̊F
Test yourself: Temperature Conversion
Consider the interval from 20 ̊F to 80 ̊F.
Calculate the equivalent temperature in ̊C and the interval between them.
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Example: Temperature Conversion
The specific heat capacity of toluene is given by following equation:
Cp = 20.869 + 5.293 × 10-2 T
where Cp is in Btu/(lb mol) (° F), and T is in ° F.
Express the equation in cal/(g mol) (K) with T in K.
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Chapter 5: Pressure
Objectives
1. Define pressure, atmospheric pressure, barometric pressure, standard pressure,
and vacuum.
2. Explain the difference between absolute and relative (gauge pressure).
3. Convert from gauge to absolute pressure and vise versa.
4. Convert a pressure measured in one set of units to another set.
5. Calculate the pressure from the density and height of a column of static fluid.
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Pressure
Pressure is defined as the amount of force exerted on a unit area of a substance.
Pressure units are force units divided by area.
force
N
P
 2  Pa
area
m
Unit
Definition or Relationship
1 pascal (Pa)
(SI)
1 kg.m-1 s-2 (N/m2)
1 bar
(SI)
1 x 105 Pa
1 atmosphere (atm)
(AE)
101,325 Pa
1 torr
(SI)
1 / 760 atm
760 mm Hg
(AE)
1 atm
14.696 lbf/in.2 (psi)
(AE)
1 atm
The pressure at the base of a vertical column of fluid of density
ρ and height h is called the hydrostatic pressure, and is given
by:
P
force F

 P  ( Ahg / A)  P  gh
area
A
h(m)
where, P₀ is the pressure exerted on the top of the column and g is
the acceleration of gravity.
P₀(N/m2)
A(m2)
P(N/m2)
Fluid density
ρ (kg/m3)
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The Barometer and atmospheric pressure
Atmospheric pressure is measured by a device called a barometer; thus, the
atmospheric pressure is often referred to as the barometric pressure.
Vacuum
Patm  W / A
W  mg  Vg  gAh
Patm  gh
A frequently used pressure unit is the standard atmosphere, which
is defined as the pressure produced by a column of mercury 760 Patm
mm in height at 0°C (ρHg = 13,595 kg/m3) under standard
gravitational acceleration (g = 9.807 m/s2).
•1 Atmosphere
•33.91 ft of water (ft H20)
•14.696 psi (lbf / in.2)
•29.92 in Hg
•760 mm Hg
•1.013 X 105 Pascal (Pa)
•101.3 kPa
The basic barometer.
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Manometer
It is commonly used to measure small and moderate pressure
differences. A manometer is a U-shaped tube partially filled with
one or more fluids of known density such as mercury, water, alcohol,
or oil. Liquids are incompressible i.e. their density is assumed to be
constant. The difference between the pressures can be calculated
from the measured difference between the liquid levels in each
arm.
The fluid pressure must be the same at any two points at the same
height in a continuous fluid :
P2  Patm  gh
P3  Patm
Test yourself:
P3=Patm
P  P1  P3  gh
P1  P2
What is the pressure 30 m below the surface of a lake? Atmospheric pressure is 10.4 m
H2O and the density of water is 1000 kg/m3. Assume that g is 9.807 m/s2.
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Pressure measurement
Pressure, like temperature, can be expressed using either an absolute or a relative scale
depends on the nature of the instrument used to make the measurements.
Absolute pressure: It is measured relative to absolute vacuum
(i.e., absolute zero pressure). A close-end manometer would
measure an absolute pressure.
Relative (gauge) pressure:
It is measured relative to ∆h=
atmosphere pressure. An open end manometer would 40.90 cmHg
measure a relative (gauge) pressure.
Vacuum pressures: Pressures below atmospheric pressure.
Absolute Vacuum
N2
Absolute pressure
Air
Patm
∆h=
11 in. Hg
Pabsolute = Patmospheric - Pvac
Pabsolute = Pgauge + Patmospheric
N2
Relative pressure
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Measurement of Pressure Differences
Apply the basic equation of static fluids to both legs of manometer, realizing that:
P2  P3
Orifice
P2  Pa   b g ( Z m  Rm )
P3  Pb   b g ( Z m )   a gRm
Pa  Pb  g Rm (  a  b )
Example:
A U-tube manometer is used to determine the pressure drop across an orifice meter. The liquid flowing in
the pipe line is a sulfuric acid solution having a specific gravity (60°/60°) of 1.250. The manometer liquid is
mercury, with a specific gravity (60°F/60°F) of 13.56. The manometer reading is 5.35 inches, and all parts of
the system are at a temperature of 60°F. What is the pressure drop across the orifice meter in psi ?
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Example: Pressure Differences
The barometric pressure is 720 mm Hg. The density of the oil is 0.80 g/cm3 . The density of
mercury is 13.56 g/cm3 . The pressure gauge (PG) reads 33.1 psig. What is the pressure in kPa
of the gas ?
3 in
Gas
12 in
20 in
24 in
Hg
Oil
16 in
3 in
PG
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