(800) 363-2264 info@rdccontrol.com Custom Assemblies Engineered Solutions
  • French
Languages
  • Français
  • English
  • Home
  • Industrial Cylinders
    • Industries Served
    • Pneumatic Cylinders
    • Hydraulic Cylinders
  • Valve Actuators
    • Hydraulic Actuators
    • Industries Served
    • Pneumatic Actuators
  • Thermocouples
    • Thermocouples 101
      • Mineral Insulated Thermocouples
      • Thermocouples for Industrial Application
      • Thermocouples for the Aluminum Industry
      • Thermocouples for General Application
      • Thermowell and Protection Tube
      • Thermocouple Hardware
    • Industries Served
    • RTD’s 101
  • About Us
  • Careers
  • Contact Us
A perfect alliance between expertise and know-how A perfect alliance between expertise and know-how A perfect alliance between expertise and know-how A perfect alliance between expertise and know-how
  • Home
  • Industrial Cylinders
    • Industries Served
    • Pneumatic Cylinders
    • Hydraulic Cylinders
  • Valve Actuators
    • Hydraulic Actuators
    • Industries Served
    • Pneumatic Actuators
  • Thermocouples
    • Thermocouples 101
      • Mineral Insulated Thermocouples
      • Thermocouples for Industrial Application
      • Thermocouples for the Aluminum Industry
      • Thermocouples for General Application
      • Thermowell and Protection Tube
      • Thermocouple Hardware
    • Industries Served
    • RTD’s 101
  • About Us
  • Careers
  • Contact Us

Temperature Calculations

Home » Thermocouples » Introduction to RTD’s » Temperature Calculations
Read further about RTD’s:
  • Metal
  • Temperature Coefficient
  • Resistance Measurement
  • Possible Errors and Precautions
  • Self Heating
  • Response Time
  • Temperature Calculations
  • Advantages and Disadvantages
7

RTD Temperature Calculations

Callendar-Van-Dusen (CVD) Equation

The relationship between the temperature and ohmic value of RTD’s were calculated by Callendar, and later on, refined by Van Dusen; this is why the equation is named Callendar-Van Dusen.

tempurature-calculation-01

With RT = resistance at T°C , R0 = resistance at 0°C, = temperature coefficient at 0°C in //°C, = linearisation coefficient, = second coefficient of linearisation for negatives temperature values ( = 0 for T > 0°C).

This equation has been transformed in order to be used easily with the coefficients A, B and C given by the standard DIN 43760 (IEC 751) and the component technicals specifications with the following conversions:

tempurature-calculation-02-2

With the following conversions:

tempurature-calculation-03
Different Coefficients for (alpha)
Coefficient Value Value Value
α 0,003850 0,003926 0,003911
δ 1,4999
β 0,10863
A 3,9083e-3 3,9848e-3 3,9692e-3
B -5,775e-7 -5,870e-7 -5,8495e-7
C -4,18301e-12 -4,000e-12 -4,2325e-12

These three values represent the three principal specifications for RTD’s.

  • 0,003850 //°C: Standard DIN 43760, IEC 751, named Europeen Industrial Standard.
  • 0,003926 //°C: Require pur platinum (99,999%), named U.S. Industrial Standard.
  • 0,3911 //°C: Often named U.S. Industrial Standard.

The Callendar-Van Dusen equation permits a good linearity of RTD’s, ±0.01°C between -100°C and +100°C but the error increases rapidly with high temperatures. Furthermore, this equation calculates the resistance with temperature change; which is the opposite of the most current uses : Temperature with resistance change.

To convert the resistance value of the RTD to temperature, we are obliged to use a quad equation to the 2nd degree, which is, in sort, the reciprocal of the Callendar-Van Dusen equation, but iniquely for temperatures superior to 0°C.

tempurature-calculation-04

For temperatures inferior to 0 C, the Callendar-Van Dusen equation is too complex to reslove and the the use of successive approximations is necessary:

tempurature-calculation-05

The following table propose calculated values with the Callendar-Van Dusen equation.

Temperatures from resistance
Resistance () CVD Equation (°C) Error (%)
10.00 -219.539 0.056
15.00 -208.114 0.073
20.00 -196.572 0.032
25.00 -184.918 0.024
30.00 -173.158 0.023
50.00 -125.602 0.383
75.00 -63.329 -0.010
100.00 0.000
102.00 5.121 -0.024
103.00 7.685 -0.022
107.79 19.991 -0.012
115.54 39.998 -0.009
120.00 51.566 -0.010
123.24 59.995 -0.011
130.90 80.008 -0.012
150.00 130.447 -0.017
175.00 197.673 -0.021
200.00 266.348 -0.027
210.00 294.246 -0.029
220.00 322.397 -0.031
250.00 408.450 -0.045
275.00 482.109 -0.048
300.00 557.688 -0.055
310.00 588.491 -0.058
399.00 879.278 -0.095

We can see that the gaps of the Callendar-Van Dusen equation are limited and are found around 0,05% and 0,1% for higher temperatures.

7

RTD Temperature Calculations

Callendar-Van-Dusen (CVD) Equation

The relationship between the temperature and ohmic value of RTD’s were calculated by Callendar, and later on, refined by Van Dusen; this is why the equation is named Callendar-Van Dusen.

tempurature-calculation-01

With RT = resistance at T°C , R0 = resistance at 0°C, = temperature coefficient at 0°C in //°C, = linearisation coefficient, = second coefficient of linearisation for negatives temperature values ( = 0 for T > 0°C).

This equation has been transformed in order to be used easily with the coefficients A, B and C given by the standard DIN 43760 (IEC 751) and the component technicals specifications with the following conversions:

tempurature-calculation-02-2

With the following conversions:

tempurature-calculation-03
Different Coefficients for (alpha)
Coefficient Value Value Value
α 0,003850 0,003926 0,003911
δ 1,4999
β 0,10863
A 3,9083e-3 3,9848e-3 3,9692e-3
B -5,775e-7 -5,870e-7 -5,8495e-7
C -4,18301e-12 -4,000e-12 -4,2325e-12

These three values represent the three principal specifications for RTD’s.

  • 0,003850 //°C: Standard DIN 43760, IEC 751, named Europeen Industrial Standard.
  • 0,003926 //°C: Require pur platinum (99,999%), named U.S. Industrial Standard.
  • 0,3911 //°C: Often named U.S. Industrial Standard.

The Callendar-Van Dusen equation permits a good linearity of RTD’s, ±0.01°C between -100°C and +100°C but the error increases rapidly with high temperatures. Furthermore, this equation calculates the resistance with temperature change; which is the opposite of the most current uses : Temperature with resistance change.

To convert the resistance value of the RTD to temperature, we are obliged to use a quad equation to the 2nd degree, which is, in sort, the reciprocal of the Callendar-Van Dusen equation, but iniquely for temperatures superior to 0°C.

tempurature-calculation-04

For temperatures inferior to 0 C, the Callendar-Van Dusen equation is too complex to reslove and the the use of successive approximations is necessary:

tempurature-calculation-05

The following table propose calculated values with the Callendar-Van Dusen equation.

Temperatures from resistance
Resistance () CVD Equation (°C) Error (%)
10.00 -219.539 0.056
15.00 -208.114 0.073
20.00 -196.572 0.032
25.00 -184.918 0.024
30.00 -173.158 0.023
50.00 -125.602 0.383
75.00 -63.329 -0.010
100.00 0.000
102.00 5.121 -0.024
103.00 7.685 -0.022
107.79 19.991 -0.012
115.54 39.998 -0.009
120.00 51.566 -0.010
123.24 59.995 -0.011
130.90 80.008 -0.012
150.00 130.447 -0.017
175.00 197.673 -0.021
200.00 266.348 -0.027
210.00 294.246 -0.029
220.00 322.397 -0.031
250.00 408.450 -0.045
275.00 482.109 -0.048
300.00 557.688 -0.055
310.00 588.491 -0.058
399.00 879.278 -0.095

We can see that the gaps of the Callendar-Van Dusen equation are limited and are found around 0,05% and 0,1% for higher temperatures.

Read further about RTD’s:
  • Metal
  • Temperature Coefficient
  • Resistance Measurement
  • Possible Errors and Precautions
  • Self Heating
  • Response Time
  • Temperature Calculations
  • Advantages and Disadvantages

Address

1100, rue
Michèle-Bohec
Blainville, QC
J7C 5N5
Phone:  (450) 434-0216
Fax:  (450) 434-0219
Email:  info@rdccontrol.com

Have questions? Want some more information?

Give us your info and we'll get in touch.

    • About Us
    • Contact Us
    • Privacy Policy
    • Terms and Conditions
    ISO 9000 Certified
    • info@rdccontrol.com
    • (800) 363-2264

    1100, rue Michèle-Bohec
    Blainville, QC J7C 5N5

    ® RDC Control 2018. All rights reserved. No reproduction allowed without the consent of RDC Control.

    Start typing and press Enter to search