Experiment #1: Empirical Temperature Measurement Date: October 27th, 2014 Coworkers: OBJECTIVE The primary objective of this experiment is to investigate the thermometric properties of the typical thermometers; namely, a platinum resistance thermometer, a chromel-alumel thermocouple, a constant volume gas thermometer, and a liquidin-gas thermometer. Correlations between these thermometers are also examined, as well as the concept of a temperature scale, which is independent of the properties of individual thermometers. APPARATUS AND PROCEDURE This experiment involves a water bath which starts off at it’s ice point and it is gradually heated to its steam point. Along the way various points are read on different sorts of thermometers including a regular alcohol and glass thermometer, a constant volume (CV) gas thermometer, a thermocouple and a platinum resistance temperature device.

• Applied Thermodynamics Lab Manual

This lab analyzes the thermometric properties of typical thermometers. We start at ice point and collect property data for four separate thermometers while increasing the temperature to the boiling point. RAW DATA Table 1: Room temperature and pressure recorded at 2pm on October 27th, 2014 Parameter Value Barometric Reading (mmHg) 665.4 mmHg ± 0.05mmHg Room Temperature (OC) 22.2 oC ± 0.05oC Converting the barometric pressure from mmHg to kPa:./0 123 P = 665.4mmHg x = 88.713 kPa 45- 6678 Table 2: Raw data for Experiment 1. Figure 1: Graph of all different types of measurements instruments versus the thermocouple. TREATMENT OF RAW DATA AND RESULTS Empirical temperature in oCalgary: Empirical temperature measurements are made using a thermometer in conjunction with an empirical temperature scale based on an arbitrary “fundamental interval” between two known different thermal levels. We can determine the temperature in oCalgary by using the formula:: 2 + 𝑊:= 2 Where: 𝑊J = Uncertainty of it’s respective subscript Combining the two formulas gives us the equation for 𝑊A: / / 𝑊A = ±𝜃 𝑊:; + 𝑊:= / / 𝑋A − 𝑋- / + 𝑊: + 𝑊:= 𝑋,- − 𝑋- / Where all of these symbols have been defined in previous formulas used to make up this equation. A sample calculation for the uncertainty in alcohol in glass would give us: / / 1/ + 1/ 1/ + 1/ 𝑊A = ±5.52 + 42 − 32 213 − 32 𝑊A = ± 0.78 oCal Table 3: Recorded value converted the empirical temperature in ℃al and the uncertainties.

Applied Thermodynamics Lab Manual

Advanced calculus angus taylor solutions manual. Empirical Temperature Uncertainty of Recorded Value (mm) (℃al) Calculation ((℃al) 32 0.00 - 42 5.52 0.78 62 16.57 0.79 82 27.62 0.81 102 38.67 0.84 121 49.17 0.87 141 60.22 0.91 160 70.72 0.96 180 81.77 1.01 202 93.92 1.07 213 100.00 1.10 The same sample calculations can be done for the other thermometers and their respective uncertainties. Temperature for constant volume thermometer:: + 𝑊:= + 𝑋,- − 𝑋/ / / 0.005/ + 0.005/ 0.005/ + 0.005/ 𝑊A = ±5.10 + 45.88 − 43.55 89.20 − 43.55 𝑊A = ±0.0155 ℃al All these values can then be tabulated. Table 4: Recorded values of the constant volume thermometer with the empirical temperature in ℃al and uncertainties. Recorded Value Empirical Uncertainty of Calculation (kPa) Temperature (℃al) (±℃al) 43.55 0.00 0.0000 45.88 5.10 0.0155 51.44 17.28 0.0157 56.56 28.50 0.0161 61.79 39.96 0.0167 66.54 50.36 0.0173 71.56 61.36 0.0182 76.42 72.00 0.0191 81.31 82.72 0.0201 86.57 94.24 0.0213 89.2 100.00 0.0219 Temperature for Resistance Temperature Device:: + 𝑊:= + 0.005/ + 0.005/ 10.264 − 10.074 𝑋,- − 𝑋/ + / 0.005/ + 0.005/ 13.799 − 10.074 / 𝑊A = ±0.0190 ℃al Table 5: Recorded values of the resistance temperature device (RTD) with the empirical temperature in ℃al and uncertainties. Empirical Uncertainty of Recorded Value (Ω) Temperature (℃al) Calculation (±℃al) 10.074 0.00 0.0000 10.264 5.10 0.0190 10.721 17.37 0.0193 11.139 28.59 0.0197 11.569 40.13 0.0205 11.957 50.55 0.0213 12.365 61.50 0.0223 12.762 72.16 0.0234 13.158 82.79 0.0246 13.585 94.26 0.0261 13.799 100.00 0.0268 Temperature of thermocouple:: + 𝑊:= + 0.005/ + 0.005/ 0.227 − 0.04 𝑋,- − 𝑋/ + / 0.005/ + 0.005/ 4.147 − 0.04 / 𝑊A = ±0.0172 oCal Tabulated values: Table 6: Recorded values of the thermocouple with the empirical temperature in ℃al and uncertainties.

Empirical Temperature Uncertainty of Calculation Recorded Value (mV) (℃al) (±℃al) 0.04 0.00 0.0000 0.227 4.55 0.0172 0.689 15.80 0.0174 1.125 26.42 0.0178 1.584 37.59 0.0184 2.006 47.87 0.0191 2.463 59.00 0.0200 2.918 70.08 0.0210 3.384 81.42 0.0222 3.897 93.91 0.0236 4.147 100.00 0.0243 Deviation from CV Gas Thermometer According to Table 3, 4, 5 and 6, the uncertainty values of the constant volume are the smallest and we can therefore assume that the constant volume thermometer is the most accurately measuring device. Every other thermometer is then compared to this one. We can determine the deviation using the following equation: 𝑑 = 𝜃 − 𝜃 Y Where: d = Deviation (℃al) 𝜃 = Temperature of the thermometer being compared (℃al) 𝜃 Y = Temperature of the CV thermometer (℃al) Sample Calculation: This sample calculation applies to all the other three thermometers except for control volume thermometer as we are using that as the standard to compare all other thermometers with. The deviation of alcohol in glass at 42mm is: d = 5.52℃al – 5.10 oCal d = 0.42 oCal The uncertainty calculation is as follows: / 𝑊 = ± 𝑊A/ + 𝑊 Y Where: 𝑊 = Uncertainty of deviation (oCal) 𝑊A = Uncertainty of temperature being compared (oCal) 𝑊 Y = Uncertainty of corresponding CV temperature (oCal) Selecting the from the same batch of values that we did above we will receive this: / 𝑊 = ± 𝑊A/ + 𝑊 Y 𝑊 = ± 0.78/ + 0.0155/ 𝑊 = ±0.78 oCal Table 7: The deviation of values from each type of thermometer to constant volume temperature in oCal with the highest values highlighted. Constant Deviation for Deviation for the Temperature of the Volume alcohol and glass resistance temperature thermocouple Temperature (oCal) device (oCal) (oCal) (oCal) 0 0.00 0.00 0.00 5.1 0.42 0.00 0.55 17.28 0.71 0.09 1.48 28.5 0.88 0.09 2.08 39.96 1.29 0.17 2.37 50.36 1.19 0.19 2.49 61.36 1.14 0.14 2.36 72 1.28 0.16 1.92 82.72 0.95 0.07 1.30 94.24 0.32 0.02 0.33 100 0.00 0.00 0.00 Deviation from the Constant Volume Temperature (°Calgary) Table 8: The uncertainties of all the deviations with the highest deviations uncertainties highlighted.