16Thermometry

📚
THERMOMETRY
▢ Introduction:

Table 1: Thermometry Basics

Term
Meaning
Thermometry
Measurement of temperature
Thermometer
Device used to measure temperature of a body
Principle
Thermal equilibrium
Thermometric property
Measurable property sensitive to temperature change
Examples of thermometric properties
Volume, pressure, resistance, thermoelectric emf, radiation intensity, magnetic susceptibility
▢ Heat and Temperature:

Table 1: Heat vs Temperature

Feature
Heat
Temperature
Meaning
Form of energy
Degree of hotness or coldness
Molecular basis
Total sum of kinetic energy
Average translational kinetic energy
Depends on mass
Yes
No
Flow
Flows due to temperature difference
Does not flow
Origin
Molecular vibration
Thermal state of body
▢ Thermal Equilibrium:
❖ Definition: Two bodies are in thermal equilibrium when no heat flows from one body to another
❖ Condition: Same temperature
❖ Thermometry Basis: Temperature measurement is based on thermal equilibrium
▢ Cryogenics and Pyrometry:

Table 1: Temperature Ranges

Term
Meaning
Cryogenics
Production and measurement of very low temperature below 77 K
Pyrometry
Production and measurement of very high temperature above 1000 K
▢ Types of Thermometers by Thermometric Substance:

Table 1: Thermometer Classification

Type
Examples / Points
Solid thermometers
Platinum resistance thermometer, radiation pyrometer, magnetic thermometer, thermoelectric thermometer
Liquid thermometers
Mercury thermometer, alcohol thermometer
Gas thermometers
Constant volume gas thermometer, constant pressure gas thermometer, vapour pressure thermometer
❖ Liquid Thermometric Substance Properties:
  • •
    Low specific heat
  • •
    High thermal conductivity
  • •
    Constant coefficient of expansion over large temperature range
❖ Why Mercury is Preferred:
  • •
    Large and uniform expansion
  • •
    High thermal conductivity
  • •
    Low specific heat
❖ Gas Thermometer Sensitivity: Gas thermometers are more sensitive than liquid and solid thermometers because expansion of gases is greater
▢ Temperature Scales:

Table 1: Common Temperature Scales

Scale
Symbol
LFP
UFP
No. of divisions
Celsius
°C
0°C
100°C
100
Fahrenheit
°F
32°F
212°F
180
Kelvin
K
273.15 K
373.15 K
100
Reaumur
°R
0°R
80°R
80
Rankine
°Rn
492°Rn
672°Rn
180
❖ Conversion Formula: \(\frac{C-0}{100}=\frac{F-32}{180}=\frac{K-273.15}{100}=\frac{R-0}{80}=\frac{R_n-492}{180}\)
❖ Temperature Difference Relation: \(\Delta1^\circ C=\Delta1K=\Delta1.8^\circ F=\Delta0.8^\circ R=\Delta1.8^\circ R_n\)
❖ Absolute Zero: \(0K=-273.15^\circ C\)
▢ Types of Thermometers:

Table 1: Thermometers: Principle, Formula and Range

Thermometer
Thermometric substance
Measurable quantity
Principle
Formula
Range
Mercury thermometer
Mercury
Change in volume/length
Thermal expansion of liquid
\(t=\frac{V_t-V_0}{V*{100}-V_0}\times100^\circ C\)
-35°C to 357°C
Alcohol thermometer
Alcohol
Change in length
Thermal expansion of liquid
\(t=\frac{l_t-l_0}{l*{100}-l_0}\times100^\circ C\)
-110°C to 76°C
Constant volume gas thermometer
Hydrogen / helium / nitrogen
Pressure
Gay-Lussac's law: at constant volume, \(P\propto T\)
\(t=\frac{P_t-P_0}{P*{100}-P_0}\times100^\circ C\)
-268°C to 1500°C
Constant pressure gas thermometer
Gas
Volume
Charles' law: at constant pressure, \(V\propto T\)
\(t=\frac{V_t-V_0}{V*{100}-V_0}\times100^\circ C\)
-268°C to 500°C
Platinum resistance thermometer
Platinum
Resistance
Resistance of metal varies with temperature / Wheatstone bridge
\(t=\frac{R_t-R_0}{R*{100}-R_0}\times100^\circ C\), \(R_t=R_0(1+\alpha t)\)
-200°C to 1200°C
Thermoelectric thermometer
Thermocouple
Thermo-emf
Seebeck effect
\(e=At+Bt^2\)
-200°C to 1600°C
Total radiation pyrometer
Radiating body
Intensity of radiation
Stefan's law
\(E=\sigma T^4\)
800°C to 4000°C
Vapour pressure thermometer
Liquid vapour / helium
Saturated vapour pressure
Vapour pressure depends on temperature
\(\log P=a+bT+\frac{c}{T}\)
0.71 K to 122 K
Magnetic thermometer
Ferromagnetic substance
Magnetic susceptibility \((\chi)\)
Curie's law: \(\chi\propto\frac{1}{T}\)
—
Below 1 K
▢ Liquid Thermometers:
❖ Mercury Thermometer:
  • •
    Based on thermal expansion of mercury
  • •
    Cannot measure much above 350°C because mercury starts vaporizing
  • •
    Can measure up to 500°C if nitrogen gas at high pressure is filled above mercury column
  • •
    Mercury has low specific heat and high conductivity
❖ Alcohol Thermometer:
  • •
    More sensitive than mercury thermometer
  • •
    Alcohol expands about seven times more than mercury
  • •
    Greater expansion gives better accuracy
  • •
    Useful for low temperature measurement
❖ Bulb Shape: Liquid thermometers with cylindrical bulbs are more sensitive than spherical bulbs because cylindrical bulbs have larger surface area
▢ Gas Thermometers:
❖ Key Points:
  • •
    Most sensitive thermometer
  • •
    Standard thermometer
  • •
    Used to calibrate other thermometers
  • •
    Constant volume gas thermometer measures temperature most accurately
❖ Constant Volume Gas Thermometer:
  • •
    For constant volume gas thermometer, gas should be at high temperature and low pressure
  • •
    Hydrogen cannot be used above 500°C because it starts diffusing
▢ Resistance Thermometer:

Table 1: Platinum Resistance Thermometer

Point
Description
Principle
Resistance of metal changes with temperature
Formula
\(R_t=R_0(1+\alpha t)\)
Temperature coefficient
High and positive
Accuracy
Most accurate thermometer of lower range except gas thermometer
Use
Measures temperature inside motor engine
▢ Thermoelectric Thermometer:

Table 1: Thermoelectric Thermometer

Point
Description
Thermometric substance
Thermocouple
Principle
Seebeck effect
Thermometric quantity
Thermo-emf
Formula
\(e=At+Bt^2\)
Use
Rapidly changing temperature
▢ Radiation Pyrometer:

Table 1: Total Radiation Pyrometer

Point
Description
Principle
Stefan's law
Formula
\(E=\sigma T^4\)
Use
Very high temperature measurement
▢ Special Thermometers:

Table 1: Special Thermometers

Thermometer
Use
Six's thermometer
Measures minimum and maximum temperature simultaneously
Beckmann's thermometer
Measures boiling point / small temperature difference accurately
Magnetic thermometer
Measures temperature below 1 K
Radiation pyrometer
Measures very high temperature
▢ Common Readings of Scales:

Table 1: Common Temperature Readings

Scales
Common reading
Celsius and Fahrenheit
-40°
Celsius and Reaumur
0°
Fahrenheit and Reaumur
-25.6°
Celsius and Kelvin
Never common
Fahrenheit and Rankine
Never common
▢ Effect of Scale on Specific Heat:
❖ Point: If temperature scale is changed from °C to °F, numerical value of specific heat decreases
❖ Reason: \(\Delta C=\frac{5}{9}\Delta F\)
▢ Read and Digest:

Table 1: Important Thermometry Points

Fact
Answer
Celsius-Fahrenheit common reading
\(-40^\circ C=-40^\circ F\)
Celsius-Reaumur common reading
\(0^\circ C=0^\circ R\)
Fahrenheit-Reaumur common reading
\(-25.6^\circ F=-25.6^\circ R\)
Kelvin scale
No negative temperature
Absolute zero
\(0K=-273.15^\circ C\)
Most accurate temperature measurement
Constant volume gas thermometer
Gas thermometer
Standard thermometer
Mercury thermometer upper limit
357°C
Mercury thermometer with high-pressure nitrogen
Can measure up to about 500°C
Alcohol thermometer sensitivity
More sensitive than mercury
Alcohol expansion
About 7 times mercury
Hydrogen above 500°C
Cannot be used because it diffuses
Six's thermometer
Maximum and minimum temperature
Beckmann's thermometer
Boiling point / small temperature difference
▢ High-Yield Recall:

Table 1: Thermometry One-Liners

Fact
Answer
Thermometry
Measurement of temperature
Thermometer
Measures temperature
Temperature measurement principle
Thermal equilibrium
Heat
Form of energy
Temperature
Degree of hotness or coldness
Cryogenics
Temperature below 77 K
Pyrometry
Temperature above 1000 K
Thermal equilibrium
No heat flow between bodies
Celsius LFP-UFP
0°C to 100°C
Fahrenheit LFP-UFP
32°F to 212°F
Kelvin LFP-UFP
273.15 K to 373.15 K
Reaumur LFP-UFP
0°R to 80°R
Rankine LFP-UFP
492°Rn to 672°Rn
Temperature difference relation
\(1^\circ C=1K=1.8^\circ F=0.8^\circ R=1.8^\circ R_n\)
Mercury thermometer principle
Thermal expansion of mercury
Alcohol thermometer range
-110°C to 76°C
Mercury thermometer range
-35°C to 357°C
Constant volume gas thermometer principle
\(P\propto T\) at constant volume
Constant pressure gas thermometer principle
\(V\propto T\) at constant pressure
Platinum resistance thermometer principle
Resistance varies with temperature
Thermoelectric thermometer principle
Seebeck effect
Radiation pyrometer principle
Stefan's law
Vapour pressure thermometer
Saturated vapour pressure depends on temperature
Magnetic thermometer principle
Curie's law
Celsius-Fahrenheit common point
-40°
Kelvin negative temperature
Not possible
Most sensitive thermometer
Gas thermometer
Very high temperature thermometer
Radiation pyrometer
Below 1 K thermometer
Magnetic thermometer
Q1.
A thermometer reads 140°F. What is the reading in Celsius scale?
📅BP 2012
Q2.
-50°C in Kelvin scale is:
📅MOE 2009
Q3.
A faulty thermometer reads 1°C at ice point and 99°C at boiling point. Correct temperature at 25°C reading:
📅IOM 2012
Q4.
Faulty thermometer has LFP=5°C and UFP=95°C. Correct temperature at 35°C reading:
📅IOM 2014
Q5.
Gas thermometer at constant volume is filled with gas at:
📅KU 2012
Q6.
Convert 98.4°F to Celsius:
📅KU 2010
Q7.
Range of common mercury thermometer:
📅IOM 04•KU 2010
Q8.
40°C equals:
📅IOM 2000•KU 2017
Q9.
Absolute zero temperature is:
📅IOM 96
Q10.
Hail stones are produced by:
📅IOM 1995
Q11.
Maximum measurable temperature with mercury thermometer:
📅BPKIHS-08
Q12.
69.8°F equals:
📅BPKIHS-97
Q13.
Temperature where Celsius and Fahrenheit scales match:
📅BP 2010•MOE 2012
Q14.
Fahrenheit reading is 3 times Celsius reading in hot bath. Temperature is:
Q15.
Temperature scale that's never negative:
Q16.
Fall in temperature when Fahrenheit reading drops from 212°F to 140°F (in °C):
Q17.
Temperature when mercury thread is 40mm above LFP (total range=160mm):
Q18.
Temperature at 60cm Hg pressure in gas thermometer (50cm at 0°C, 90cm at 100°C):
Q19.
Temperature when resistance is 3.26Ω (2.71Ω at 10°C, 3.70Ω at 100°C):
Q20.
Temperature when resistance doubles (α=0.00125/°C, R=1Ω at 300K):
Q21.
Correct temperature when faulty thermometer (50-95 range) reads 59:
Q22.
Temperature measured by thermometer Y when X reads 60°C (X:15-75, Y:25-125):
Q23.
Boiling point on faulty thermometer (ice at -10°C, 60°C instead of 50°C):
Q24.
Smallest detectable temperature (40μV/°C, 10Ω, 1μA):
Q25.
Resistance at 50°C (6.74Ω at 0°C, 7.74Ω at 100°C):