LABORATORIES NUMBER 5 AND 6

 

 MEASUREMENT OF TEMPERATURE AND PRESSURE

 

1.0 INTRODUCTION      San Francisco State University, School f Engineering    © 2000 A. J. Wheeler

 

The purpose of this laboratory is to introduce the student to two common devices used to measure temperature and pressure - the thermocouple and the pressure transducer. In addition, the student will use the computerized data acquisition system to measure the response of a simple thermal transient system.

 

2.0 MEASUREMENT OF TEMPERATURE

 

 2.1 EXPERIMENTAL EQUIPMENT

 

The apparatus consists of two thermocouples, connected in a standard reference junction configuration, a hot plate, a container of water, a mercury-in-glass thermometer and a voltage-temperature conversion table for type K thermocouples. Also available is an infrared (IRI hand held thermometer. This instrument is an Extech Model. 42520 Infrared  (IR) thermometer. The specifications are included in the supplementary information for this lab.

 

 2.2 EXPERIMENTAL PROCEDURE

 

Write down your answers to each of the questions asked in the sections below.

 

1) Connect the thermocouples to the DMM. Wave the thermocouples around in the air for a minute or so and then record the voltage. Look up the temperature in the table. The temperature should be close to zero (at least under a degree). What does the temperature you measured represent? It should be noted that this is not quite the correct use of the tables since the tables assume one junction is at 0 C and the calibration will be slightly in error at the higher room temperature reference temperature.

 

2) Grip on of the junctions in one hand for a minute or so. Record the voltage. Is the voltage positive or negative? What does the sign of the voltage mean here?

 

3) Prepare the ice bath by mixing crushed ice and water. A correctly prepared ice reference bath must be a slushy mixture of water and ice and the ice must extend all the way to the bottom of the container. If the ice floats on some water, the water below the ice may have a temperature greater than 0 C since water is most dense at a temperature of 4 C.

 

4) Place one of the junctions in the ice bath (select the one that causes the DMM to read positive). Prepare a data sheet with the following columns:

 

                      RUN    TC mVOLTS    TC TEMP     Hg TEMP   IR Temp (B)   IR Temp (SS)

 

Place a container of cold water on the hot plate and insert the other junction into it. Place the mercury-in-glass thermometer in the water. Turn on the hot plate. About every two minutes, read the DMM and the thermometer and record the data. Also measure the temperature of the container using the IR thermometer and record the results as discussed below. It is best if you use the thermometer to stir the water ever thirty seconds or so. Continue for about 10 minutes.

 

As you heat the water and measure the Hg in glass thermometer and the thermocouple output, you are also to make two measurements using the IR thermometer. The temperature of the stainless steel water container will be about the same as the water inside. On the side of the water container is an area painted flat black. Holding the thermometer about six inches away, point it at the center of the black area and press the button and take a reading (B). Next, point it at an unpainted area (stainless steel, SS) and take a reading. It should be noted that the black area has an emissivity on the order of 0.9 whereas the unpainted area is much lower, perhaps 0.1 in the infrared range. Record these readings on your data sheet.

 

Compute the thermocouple temperatures from the tables, and compute the % difference between the thermocouple temperature and the mercury-in-glass thermometer temp. What do you think about the agreement? Do the same for the IR thermometer readings.

 

 

3.0 MEASUREMENT OF A TEMPERATURE TRANSIENT

 

3.1 EXPERIMENTAL EQUIPMENT

 

The apparatus consists of the data acquisition system, an ice reference bath, and two sets of thermocouples connected in the standard reference configuration. The difference between the two thermocouple sets is the diameter of the sensing (not the reference) junction. In one case, it is 1/8 inch diameter and in the other it is 1/16 inch diameter. The output of each thermocouple pair is connected to the DAS.

 

3.2 EXPERIMENTAL PROCEDURE

 

Both reference junctions should be placed in the ice bath and the other two junctions should be at room temperature. The transient we are studying is simple. At the start, both sensing thermocouples will be placed into the ice bath also. They will then proceed to cool down to the temperature of the ice bath. The smaller diameter thermocouple should respond more rapidly.

 

Turn on the computer and start MATLAB. Put your formatted disk in drive A: Type temptran at the >> prompt.  At the prompt, enter the name of the file to save the data (e.g. a:myfile.txt).

Temptran samples channels 0 and 1 for the small and large thermocouple respectively. At the starting prompt, press d but do not press Enter. Then press enter and immediately thrust the two thermocouples into the ice bath. A plot of your data should appear in the upper left hand side of the screen.

 

Load the EXCEL spreadsheet. Import the file you created above into the spreadsheet.  You will have three long columns of numbers. The first is time, the second is the temperature of the large thermocouple and the third is the temperature of the small thermocouple. Make a plot of temperature versus time. Put both temperatures on the same scatter plot - the large T/C data and the smaller T/C data. Use the lines only option of the scatter plot (i.e. do not include the data points, there are too many of them and they will confuse the plot).

 

You have now taken all the data. You are now to evaluate a time constant. It is expected that the temperature will drop according to:

 

 

where T is the measured temperature difference, Ti is the initial temperature difference, t is time and is the time it takes the temperature to decrease to 1/e of its initial value (the time constant).

 

This equation is for temperature. In fact, the temperature is not a linear function of voltage and before we examine temperature response, we should convert our data from mV to degrees. However, for the limited range of temperatures in this problem (20C to 0C), temperature is approximately a linear function of voltage and so we can evaluate the time constants using the voltage data directly.

 

Pick a point in time on the graph close to time zero but after the temperature has started to drop. Call this ti and Ti. Find, at a later time the value of time, tf ,where the temperature is 1/e (i.e. 0.36788) times Ti. The time constant is (tf - ti). Evaluate for the large and small thermocouples from the computer plot. Are the results as expected?

 

 

4.0 MEASUREMENT OF PRESSURE

 

4.1 EXPERIMENTAL EQUIPMENT

 

In this experiment, you will measure pressure using three devices - a pressure transducer connected to the data acquisition system, a mercury manometer and a direct reading pressure gage. Most pressure gages are called Bourdon gages. The particular gage used in this experiment is actually a diaphragm type which is more expensive and generally more accurate. All three of these instruments are connected together and sense the same pressure. The pressure is supplied by a hand operated inflation bulb from a blood pressure set (the mercury manometer and pressure gage also come from blood pressure sets).

 

The most inherently accurate instrument in this setup is the mercury manometer. Its accuracy is only dependent on the measurement of the length of the mercury column and the density of the mercury. The pressure difference required to support the column is:

 

 

Where P is the pressure difference in pascals,  is the density of mercury (kg/m3), H is the height of the column in meters and g is the acceleration of gravity (9.8 m/s2). The pressure gage also reads in mm of mercury. This is not a normal units for a pressure gage but this is a special gage intended for a blood pressure set.

 

The pressure transducer has an output in mvolts. The pressure transducer (described in the attached data sheet) is an inexpensive one and although it should be repeatable and linear in output, its calibration is not claimed to be better than 5%. The output is specified as 79 mV for a 30 psi (206,850 Pa) pressure differential with a 10 volt power supply. This 30 psi pressure corresponds to 1551 mm Hg. Expressed in a different way, the pressure transducer should have an output of 5.0910-3 mV/mmHg-Volt of the power supply.

 

The power supply consists of a nominal six volt lantern battery.

 

 

4.2 EXPERIMENTAL PROCEDURE

 

Measure the voltage of the power supply battery with a multimeter while it is connected to the transducer.

Open the valve on the bulb so that the pressure is zero. Check to see that the pressure gage and the manometer read zero. If either shows a substantial discrepancy, show the instructor. It is possible that the technician can adjust them. Note: When increasing the pressure, pump the bulb slowly. If the mercury column rises too rapidly, it can leak out.

 

Turn on the computer and, start Matlab, and type pressure at the >>prompt. This M-file measures the battery voltage on channel 1 and the transducer output on channel 2. Each time it takes a reading, it takes 100 samples at 1000 samples per sectond. The 100 samples are averaged for the final result. Enter the file to save the data at the prompt. Pump up the manometer to 280 mm Hg. At the prompt, type d and press Enter. At the prompts, enter the values of the manometer and bourdon gage readings. Repeat for readings of 200, 100, 50,  25 and 0 mmHg. For the zero reading, leave the valve of the bulb open regardless of the manometer reading.  The plot on the screen shows the transducer output as a function of the manometer reading. Terminate the data taking. Save the results on a disk if you want to do the following calculations using the spreadsheet program instead of by hand.

 

One problem with pressure transducers like this is that while the slope of the voltage output will remain quite stable with time, the reading with zero applied pressure may change. This is known as a zero offset. We need to correct the pressure transducer output for this zero offset. Create a sixth column which is the transducer output minus the reading at zero pressure.

 

Create a seventh column on the data sheet. This is the pressure from the transducer in mmHg. This is obtained by dividing the corrected transducer voltage by the product of the above calibration constant (5.0910-3) and the power supply voltage. This is now the transducer output in mmHg. Treating the manometer as the primary measurement, compute the percentage error for the pressure gage and the transducer in columns 7 and 8. Print the spreadsheet.

 

 5.0 REQUIRED RESULTS

 

Your data sheet and question answers from Part 2

 

Your plot from Part 3 and on a separate, identified sheet of paper, your calculations and two values of , the thermocouple time constants.

 

Your table of pressures and percent errors from part 4.0.

 

On a separate sheet, your response to the following questions

 

1) Do you think your electrical measurements for part 2 would have produced significantly different temperatures if you had used an RTD or a thermistor device?  What about part 3? Why?

 

2) Which thermocouple responds more quickly? Can you give some reasons why?

 

3) What can you say about the accuracy of the pressure transducer? The pressure gage? What can you say about the linearity of the pressure transducer and the pressure gage?

 

SUPPLEMENTARY INFORMATION FOR LABORATORIES 5 AND 6

 

MEASUREMENT OF TEMPERATURE AND PRESSURE

 

 1.0  TEMPERATURE MEASUREMENTS

 

 1.1 INTRODUCTION

 

There are four main types of devices with electrical output which are used for measuring temperatures in the moderate temperature regime. These are Thermocouples, Resistance Temperature Detectors (RTD's), Thermistors and other Semiconductor Devices. As temperatures become very high, these devices are damaged or destroyed and other methods must be used, radiation pyrometers being common.

 

In selecting a temperature measuring device, the user must consider a number of factors such as durability, stability (i.e. its temperature- voltage characteristic remains constant over time), transient response time, physical size, level of output voltage, purpose of the output etc. Often, more than one of the devices will be appropriate.

 

1.2 THE THERMOCOUPLE

 

 

Figure 5.1 - TC voltage vs. temperature

When two different metals are brought into intimate contact (as by welding for example), a voltage difference will be created across the junction as a result of the Seebeck Effect>. The voltage that is developed is a function of the temperature of the junction and so this simple device is a temperature sensor.

 

Different combinations of metals produce different voltage levels and different temperature coefficients (mV/C etc.) but certain metal combinations have been found to work best and are sold commercially. The voltage characteristics of some of these are shown in Figure 5.1. Some examples of standard thermocouple pairs are Platinum/Platinum-Rhodium, Iron/Constantan, Copper/Constantan and Chromel/Alumel. Most of these metals are alloys. Generally, a high temperature coefficient is wanted but the thermocouple must survive in the measurement environment. For example, copper/constantan has a high voltage output but will be destroyed at high temperatures or in chemically harsh environments. Platinum/Platinum-Rhodium has a rather low voltage output but is stable in some rather active chemical environments.

 

With the restricted combinations of metals used, it is possible to standardize thermocouples. Companies that manufacture thermocouple junctions and lead wires take great care to control the composition of the materials. It is thus possible to purchase thermocouples and wire, use standard tables to convert voltage to temperature and have a high confidence that the temperature measurement is accurate. At San Francisco State, virtually all the thermocouples are of the Chromel/Alumel type. This type, often called "Type K", is durable at temperatures up to 1300 C, and has a fairly high temperature coefficient.

 

Thermocouple junctions can be made in very small sizes - as small as 0.0005 inches is possible. This makes it possible to get very good spatial resolution of temperature and to measure time-varying temperatures to 0.1 seconds or better.

 

Figure 5.2 - Thermocouple connected to DVM

Figure 5.3 - TC with ice reference

Reliability and relatively low cost have made thermocouples extremely popular as temperature measuring devices. However, they do have some complications. In Figure 5.2, a copper-constantan thermocouple is shown connected to a voltmeter to measure the temperature at J1. A problem becomes immediately apparent. While there is a copper-constantan junction at J1, there is also a copper-constantan junction at J2. The secondary junction at J2 also produces a voltage and so the measured voltage is not simply the voltage change at J1. It can be demonstrated that the measured voltage is directly related to the temperature difference (TJ1 - TJ2). To make this system work, an independent measurement of the temperature at J2 is required. A better way to measure temperature J1 is shown in Figure 5.3. In this case, the point J2 is known as a reference junction. The junction at J2 is normally maintained at a relatively easily controlled temperature, the temperature of melting distilled water being most common. This is called an "Ice Reference Junction" or simply and "Ice Reference". In the labs at SFSU, these are normally made of crushed ice and water in a thermos bottle. Commercial devices are available which will simulate an Ice Junction without the need to maintain an ice bath.

 

In the example above, the thermocouple metals were copper and constantan so the junctions at the voltmeter were copper-copper.  If the thermocouple were chromel-alumel, the junctions at the voltmeter would be copper-alumel or copper-chromel so there would be voltages generated.  If both terminals are kept at the same temperature,  these voltages cancel out.

 

In data acquisition systems, an alternate method of compensation may be used. As shown in Figure 5.4, all the thermocouples are directly connected to the data acquisition system terminal strip. The reference junction is also connected to the terminal strip. The terminal strip is insulated so that all the terminals are at the same temperature. The reference junction voltage is then arithmetically subtracted from the voltage of each of the sensing junctions to arrive at the correct voltage. Alternatively, a semiconductor temperature measuring device is used to determine the temperature of the terminal strip.

 

Figure 5.4 - TC connections to DAS

 

Thermocouples have some other difficulties also (but share these with some of the other devices). The output is in the millivolt range and hence the signals can be contaminated by electrical noise. The voltage output is also not generally a linear function of temperature and so tables or curve fits must be used to convert voltages to temperature.

 

1.3 RESISTANCE TEMPERATURE DETECTORS

 

It was mentioned in the discussion of strain gages that strain gages have to be compensated for the effects of temperature. Many Resistance Temperature Detectors (RTD's) take advantage of this effect to create a temperature sensor. Some designs in fact look a bit like small strain gages. In other cases, the sensor is a coil of wire. In any case, an RTD is a device for which the resistance is a direct function of its temperature. These resistance of these devices can be measured with a Wheatstone Bridge. The resistance is normally a non-linear function of temperature so a calibration curve is required to convert resistance to temperature. The output of the measuring bridge is in the millivolt range so there can be some problems with electrical noise. The voltage supply to the bridge must also be kept to a minimum since I2R losses in the sensor can heat the sensor and cause temperature errors. There is no need for a reference junction with these devices. They are not normally quite as small as the minimum size possible for thermocouples and do not give such good spatial resolution. They can be made of thin foils, however, and the time response can be quite rapid.

 

1.4 THERMISTORS

 

Thermistors are generally made of semiconductor materials devices which have a negative coefficient of resistance with temperature (i.e. the resistance goes down as the temperature increases). These devices are much more sensitive to temperature changes than are RTD's - the resistance can change on the order of 1% for each 1 C change in temperature. The output can be sensed with a Wheatstone Bridge but the change in resistance is so large that multimeters and other devices to measure resistance are often adequate. The output is not in general linear with temperature. Thermistors are often used to measure water temperature in automobiles. Thermistors are generally larger than the largest of thermocouple junctions and have poorer spatial resolution and somewhat slower time response. They also do not survive at very high temperatures (greater than about 300 C).

 

 1.5 SEMICONDUCTOR TEMPERATURE SENSORS

 

The voltage across a simple diode is a function of temperature. Resistance varies with temperature. Individual components or integrated circuits can be produced which have an output which is a function of temperature. In many cases the output signal can be high level (on the order of 5 volts) which has little problems with noise. Furthermore, they can often be constructed to have a linear output so that output can be readily converted to temperature (e.g. with a simple meter). Generally, these devices are not as small nor do they have the rapid time response of small thermocouples nor will they survive high temperatures.

 

1.6 THE INFRARED TEMPERATURE THERMOMETER

 

This type of device measures the temperature of a surface by measuring the infra red radiation emitted by that surface. The general theory of this device is described in Chapter 9 of the Wheeler and Ganji 300 text. In simple form, it makes use of the Stefan-Boltzmann law:

 

                                                                            [A]

 

which applies to an ideal surface known as a black body.  Eb is the radiative power in Watt/m2, T is the actual temperature in oK and s is a constant known as the Stefan-Boltzmann constant. An actual surface will radiate less energy than a black body and its radiative power is given by:

 

                                                                           [B]

 

where e is known as the emissivity of the surface and has a value between 0 and 1. Very shiny metals can have a very low emissivity, on the order of 0.02. Common surfaces such as brick and paint often have emissivity values in the vicinity of 0.9.

 

The infrared thermometer works by sensing the emitted radiation and effectively using Eq. B to estimate the temperature.

 

Since the temperature is proportional to the inverse fourth root of the emissivity,  the measurement is not that sensitive to the actual emissivity. In the Extech 42520, it is assumed that the emissivity is 0.95. More expensive IR thermometers allow the user to specify the emissivity.