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The law of nature

No matter how sophisticated the measuring instruments are, the laws of nature still prevail. Failure to take these laws into account will be penalized by unnecessarily high measuring errors. The most important of these laws are described here.

Content

 

The zeroth law of thermodynamics

Temperature measurement is based on the laws of thermodynamics, the most important of which is that known as the zeroth law of thermodynamics. Although this law was coined after the other laws of thermodynamics, it was deemed to be of such importance that it really should come first—hence the name, zeroth law. The law states the following:

"If two systems are each in thermal equilibrium with a third system, then the first two systems are in thermal equilibrium with each other."

This means that bodies at different temperatures work to equalize their temperatures. Consider the illustration to the right. The bodies are insulated from the surroundings and will assume the same temperature.

In reality, there is no perfect insulation. If one of the bodies, eg, a thermometer, is exchanging heat outside the insulation, heat will be transferred to or from the body and perfect thermal equilibrium will not be possible.

 

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This figure illustrates the zeroth law of thermodynamics. The three bodies will
assume the same temperature, i.e
they will be in thermal equlibrium. If
one of the bodies, the thermometer,
is in coummunication with the
surrondings outside the insula tion,
heat will be transferred to or from the
body, and the bodies will therefore
not be in thermal equilibrium.

 

A thermometer measures its own temperature

A thermometer can only measure its own temperature; the reading lies somewhere between the temperature of the object to be measured and that of the surroundings. It is therefore essential that thermometers be designed and installed in a way that minimizes the transfer of heat to or from the surroundings.

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A thermometer measures its
own temperature.

 

Heat transfer

Heat transfer takes place in one or more of the following ways:

  • Conduction, eg through a metal rod
  • Convection, eg natural circulation of gases and liquids
  • Radiation

Heat always passes from a body at a higher temperature to one at a lower temperature.

 

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Heat passes from a body at higher
temperature to one at a lower temperature.

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Heat transfer by convection occurs
through changes of density in a gas or liquid.

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Radiation transfers heat from a body
at a higher temperature to one at a
lower temperature.

 

Thermal shunting and thermal loads

A temperature sensor conducts heat, which gives rise to what is called thermal shunting. The problem is particularly marked when temperature measurements are being made on pipes and surfaces. The greater the temperature difference, the greater the quantity of heat that is "drawn out" of the body by the sensor.

There is a sharp drop in temperature at the point at which the sensor protrudes from the object to be measured. This is caused by a load being imposed on the object to be measured. The temperature drop is greatest when the material to be measured is a poor conductor of heat (low thermal conductivity). To overcome the problem, the point at which the sensor leaves the body to be measured must be at a suitable distance from the measuring junction.

 

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Heat is transferred from the body
being measured at the point at
which the sensor leaves the body.
This phenomenon is known as
thermal shunting. The sensor
conducts heat away from the
body, since metal is a better
conductor of heat than the sorrunding air.

 

Surface-mounted sensors

Surface-mounted sensors are particularly sensitive to thermal shunting. But they also present another problem. Suppose that a round sensor is placed in contact with a flat surface. Only a fraction of the circumference of the sensor will be in contact with the object to be measured; the rest of the sensor will be measuring the temperature of the surrounding air.

Thus, it is essential that the maximum possible contact surface be achieved between the sensor and the object to be measured.

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A round sensor placed in contact
with a flat surface. Only a fraction
of the circumference will be in
contact with the object ot be
measured, the rest of the sensor
is measuring the temperature of
the surronding air.

 

Heat due to friction

Heat due to friction is caused when a temperature sensor is placed in a strong flow of gas. The effect is the same as that occurring when you run down stairs with your hand on the bannister rail—it will get hot.

In a gas, the heat is caused by molecules colliding with the temperature sensor. When kinetic energy is retarded, heat due to friction is produced. The energy is manifest by an increase in the temperature reading.

Another example of this is what happened to the supersonic passenger aeroplane, Concorde. When it was flying over the Atlantic Ocean at Mach 2.2 at an altitude of 17,000 metres, the plane actually grew in length by 25 cm. This is because of the heat caused by friction in the cold, thin air.

 

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When the sensor is placed in a flow it measures the temperature of the gas
plus friction heat.

 

Temperature gradient

There is no clear dividing line between different temperature zones. The temperature gradient in an oven wall, for instance, falls gradually, depending on the thermal conductivity of the wall. In a homogeneous material of sufficient area, the temperature will usually fall proportionately to the thickness of the oven wall.

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In a homogeneous material of
sufficient area, the temperature
will usually fall proportionately to
the thickness of the oven wall.

 

Stem losses

Heat losses through the probe or stem occur when a sensor connects a warm zone with a colder one, especially if the sensor is the easiest path for the transfer of heat. Heat is conducted away from the object being measured and the sensor gives a lower temperature reading than the true value.

Such losses can be effectively countered if we ensure that the thermal conductivity across the probe tip is much higher than it is along the length of the sensor. In other words, more heat is transferred to the sensor probe than is conducted away through the sensor sheath.

The most usual way to avoid heat losses through a sensor sheath is to insert the probe deeper. The best solution is to improve the transfer of heat from the medium being measured to the probe. Another way is to reduce the quantity of heat being transferred by insulating the terminal head. Bear in mind that the terminal head can get hot.

 

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The sensor sheath (probe) con-
ducts heat away from the medium,
resulting in a lower temperature
reading than the true one.
The temperature drop in front of
the probe is dependant on the
flow velocity.

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Insulation of the terminal head
reduces the temperature diffe-
rence and, hence, the heat loss
through the sheath.

 

Screening

The readings made by the temperature sensor can also be disrupted by heat transfer through radiation. One example is where the temperature of gas in a tube is to be measured. The gas is warm, whereas the wall of the tube is cool.

The cold walls is within the field of view of the sensor and heat is radiated from the warm sensor. A corresponding effect occurs in the measurement of the atmospheric temperature in hot ovens, where the hot heater element radiates heat to the sensor.

Pentronic has a variety of screened sensors. We can also manufacture special screened sensors, or accessories that screen existing sensors from sources of radiation.

 

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The hot oven walls radiates heat to the
temperature sensor, producing a
temperature reading that is higher than
the true value. Pentronic solves this
issue by using different types of
screening. The reverse effect applies
when measurements are being made,
eg in pipes having a lower wall temperature.

 

Long detectors

Many resistance thermometers have physically long sensors. If the sensor is placed in a temperature gradient, the ends of the sensor will exhibit different temperatures. The measured value will be the average of the two temperatures. This needs to be taken into account both in choosing sensors and on installation.

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A thermocouple and a Pt100
detectorwill measure different
temperaturesin a temperature
gradient, even though the
insertion length are the same.
This is because the Pt100
detector measures the mean
value of the temperature
along the resistance wires.

 

Self heating

The measuring principle of platinum resistance thermometers and thermistors is that electrical resistance varies with temperature. A proportion of the measuring current applied will always be converted into heat energy.

The magnitude of self heating is largely determined by the power applied and the ability of the sensor to dissipate the heat. A large area usually facilitates heat dispersal.

The temperature of a wire-wound Pt100 will increase by a few hundredths of a degree, and that of Pt100 and Pt1000 thin-film thermometers by a few tenths of a degree. The temperature of small thermistors can increase by several tenths of a degree.

The medium in which the temperature sensor is inserted is significant; static gas, for instance, will drastically increase the self heating.

 

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The self-heating effect of the sen-
sor is determined by the resistance
and size of the sensor. The wire-
wound Pt100 sensor has the lowest
self-heating effect, whereas the
thin-film thermometer is heated
more although not as much as
small thermistors.

 

Response times

The response time depends on how long it takes for the sensor to assume thermal equilibrium with the body or medium to be measured. Critical factors include:

  • The specific heat capacity of the sensor. The greater the mass, the longer the response time.
  • The heat transfer capacity of the material. Air gaps, for example, reduce the heat transfer capacity.
  • The contact surface between the sensor and the body or medium to be measured.
  • Flow velocity and medium.

The response time can become longer over time because of changes to the material, eg, caused by high temperature. For instance, if a glue become brittle, it will gradually change to a porous powder and thus assume different heat-transfer properties.

 

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The response time of the sensor
depends on how long it takes the sensor
to reach the same temperature as the
body or medium to be measured. Fast
response requires low mass detectors
and good heat transfer properties to the sensor.

 

Why Pentronic's sensors are superior

The laws of nature are not subject to negotiation; and it is almost as difficult to depart from the DIN standards—the process coupling, dimensional and similar specifications must all be adhered to if the sensor is to be integrated into the process.

A standard Pentronic sensor is compliant with the DIN standard but follows the laws of nature better than do other makes. That's why you get a measurably superior performance from Pentronic's products.

Secrets of the Pentronic design:

The probe has a layer of metal in the tip and the detector is a "suction fit".

The detector is embedded in the metal. This gives optimum heat transfer across the probe tip, greater accuracy and a faster response.

Other advantages include greater tolerance to vibration and elimination of the need for contact paste—the sensor can therefore be installed with the probe tip uppermost.

 

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Conventional DIN type B has
insulating layers of air and
ceramic powder.

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Pentronic's temperature sensor
has the detector embedded in
metal.
This means increased accuracy,
faster response, more vibration
tolerant and elimination of the
need for contact paste.

Good transverse heat transfer

Good heat-transfer properties between the measured body or medium and the sensor are crucial to the results.

However, sensors constructed faithfully to DIN type B have two layers of insulation between the detector and the sheath: an air gap between the probe and detector insert; and ceramic powder round the detector to stop it rattling about.

 

 

Watch out for the "muesli" effect

If subjected to vibration, Pt100 sensors constructed faithfully to the DIN standard can suffer from what is known as the "muesli" effect.Vibration causes the powder surrounding the detector to move or migrate. There are two manifestations of this, depending on the design of the sensor:

  • If the tip of the probe is above the horizontal plane, the powder will run back inside the probe, leaving an air gap between the detector and the protective tube. This allows the detector to knock against the tube.
  • If the tip of the probe is below the horizontal, the powder will become packed in the tip, forcing the detector up to the top—just like raisins in a packet of muesli—and eventually breaking the wires.

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If the sensor is installed with the
probe tip down, the vibration
will cause the powder to become
compacted in the bottom of the
probe, forcing the detector back
up the probe and eventually
breaking the wires.

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If the sensor is installed with the
probe tip up, the vibration will
shake the powder away from
the tip, leaving air gaps around
the detector.

 

Shorter insertion length

The most common problem with temperature sensors is the heat loss through the protective tube or sheath. This is determined by the relationship between the heat transfer across the probe tip and the heat dissipation along the sensor body.

The DIN standard takes such heat losses into account in the specified insertion lengths, the shortest of which is 160 mm. However, in practice much shorter lengths are used, with measuring errors being the result.

The Pentronic design allows shorter lengths to be used without any increase in measuring uncertainty.

 

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The Pentronic design allows shorter
lengths to be used without any increase
in measuring uncertainty.

 

Heat dissipation

In some cases, particularly when surface temperatures are being measured, the standardized types of sensor have obvious drawbacks. It is critically important that the sensors are as small as possible, so that they do not upset the heat balance of the body to be measured.

The heat-transfer properties of the surface sensor must be appreciably greater than those of the body to be measured. What is most important is that there is good contact between the sensor and the measuring surface and thus no insulating air gaps.

 

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The heat-transfer properties of
the surface sensor must be
appreciably greater than those
of the body to be measured.

 

Reduced-diameter probe tip

The response time is determined by the time it takes for the probe tip to heat up.

Although the greater the mass the longer will be the time, the probe must be thick enough to cope with high pressures and flows.

The DIN standard represents a compromise aimed at satisfying everyone. In many applications, it is possible to reduce the probe thickness and thus improve the response time. Pentronic constructs many standard sensors with a reduced-diameter probe tip. We can produce custom sensors and tailor the probe tip to suit the pressure, flow and performance requirements.

 

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Pentronic's machine shop can
adapt sensors to customers'
own specification and for specific
sensing enviroments. A reduced
diameter probe tip for faster
response is just one example.