Purpose

The purpose of this lab is to demonstrate how thermocouples work, and to explore the concept of sensible and latent heat.

Prelab

1. Print this datasheet and bring at least one copy per group to the lab

2. Bring a USB memory key to this session.

3. Define the terms sensible heat and latent heat and explain them as they relate to the lab below.

4. Calculate the energy requirement on a mass basis to:

   • Convert 0°C ice into 0°C water

   • Heat 0°C water to 100°C water

   • Convert 100°C water to 100°C steam

Theory

We can describe the energy of any closed system, or the energy change of any closed system by a combination of its sensible and latent heat. Sensible heat is the more familiar concept, and is closely related to the temperature we can measure with a thermometer, or by touch, hence the name sensible heat. Latent heat is the energy required to change the state of a substance, and cannot be felt. This energy is used to increase the disorder or entropy of the system under consideration. A liquid is "less ordered" than a solid since it lacks a definite structure and occupies a greater volume, or is more spread out. A gas is "less ordered" than a liquid because it is even less structured and occupies a still greater volume.

In order to transition from one state to another, the transition temperature must be reached. For water, this is defined as 0°C for a solid-liquid transition, and 100°C for a liquid-gas transition. Once we reach this temperature all further energy is consumed by the phase change. No change in temperature is detected until this transition is complete (in practice some areas may be cooler or warmer than expected because heat doesn't spread instantly in real world substances). During this period, energy is being consumed, but will not be reflected in a change of temperature in the system.

The total energy required to heat water from ice to steam is thus the combination of the sensible heat and latent heat consumed over the test period.

To measure the temperature of the water, we will be using a thermocouple. The thermocouple takes advantage of the Seebeck Effect which states that an electric current will flow in a closed circuit of two dissimilar metals.

The thermocouples used in the lab have two color coded wires that are each made of a different metal, the metals vary in each thermocouple type, but the principle holds in all of them. Heat energy causes electrons to migrate from one of the metals to the other, and this flow can be measured. The greater the surrounding energy, the greater rate of migration and the greater the electric current will be. Below are the experimentally derived equations for the possible thermocouple types used in the lab. Notice that each thermocouple type experiences a different potential (voltage) over the range of test temperatures. For this reason it is important to know which type is being used.

The efficiency of a system: η = Net Work/Input Work. That is, the efficiency is a measure of useful work, where you divide the useful work done, by the total work done. In this lab, work is a measure of heat. We will divide the heat that is gained by the water by the total heat produced.

The sensible heat gained by the system is found via:

Q_w= m•C•(T_f - T_i)

where:

Q_w is the heat energy consumed by the water (kJ)

m is the mass (kg)

C is the specific heat (kJ/kg °C)

T_f - T_i is the temperature change from the final temperature to the initial temperature (°C)

The total heat produced is a function of Power consumed by the hot plate and is found via:

W_Elec = V•I•t

where:

W_Elec is the electric work supplied by the heater (kJ)

V is the voltage at the heater (V)

I is the current through the heater (A)

t is the time for which the heater was active (s)

The efficiency is then:

η = (Q_Fus+Q_w) / W_Elec

The theory above, and these equations will allow us to test the efficiency of the hot plate in delivering heat energy to the system under test.

Problem

AP Engineering Inc. is working with an apple juice supplier to determine energy requirements for a processing plant. Juice comes frozen and needs to be melted and then heated to boiling in order to pasteurize it for safe long term storage.

AP Engineering has tasked you and your team to help out in determining the amount the finance department should charge for energy consumed in the processing steps based on electric power used.

You should propose the following:

• The optimistic (theoretical) energy required to melt and bring your sample to a boil (assuming 0°C ice to 100°C water) .

• The actual energy required to boil your sample with the lidded system.

• The efficiency of your processing equipment.

Procedure

1. The measurement system is calibrated to read against room temperature.

   • You should add room temperature to any measured temperatures to compute the actual measured temperature.

2. Weigh the empty pot and record its mass.

3. Cover the bottom of the pot with ice and record its new mass (ice + pot).

4. Add enough COLD water to just cover the ice, then weigh the pot and record this third mass (water-ice mixture + pot).

   • You should have three masses: Empty pot, pot with ice, and pot with ice + water.

5. Place the pot on the hot plate and be sure that the thermocouple is in the water and not touching the bottom or sides of the pot.

6. Turn on the hot plate, set the thermostat to full and start the data collection by pressing the “Data Logging Start/Stop” on the computer screen.

   • Provide a file name and location to save the data. Ensure that the location is the Desktop and that you choose a unique filename.

   • A good filename would be: Group A - Lab 1 or whatever identifier is used for your group.

   • It is a good idea to start a "test log", let it run for a moment, and then stop it. Open this file to verify that logging is working.

   • The “Logging” indicator will be a brighter green when measurements are being saved.

7. Measure and record the power as reported by the Kill-A-Watt meter.

   • The default display is Volts, and you can press the function keys to get the power drawn.

8. Continue heating until the pot boils.

9. Once the pot has started to boil, stop the data collection by pressing the “Start/Stop” button again.

10. This will give you a file of electrical output from the thermocouple versus time for your test.

    • Save this file to your USB key.

    • Remember to calculate the temperature using the thermocouple output and according to the relations under the graph above.

11. Before leaving the lab, make sure to record the type of thermocouple used for your measurements.

12. Save the results to your USB key if you have not already done so.

Requirements

Results

• Convert your test file of electrical signals (in mV) to temperatures using Excel or similar software. Use the relations in the graph above.

  • Be sure to use an excel formula/spreadsheet for this as there are too many data points for hand processing.

• Plot a graph of temperature vs. time using the temperatures you calculated above.

• Add trendlines to your data using a single graph.

  • You should have separate trend lines for each stage of your test: melting of ice, heating the water, and boiling water.

  • Do this by graphing three different temperature ranges, broken out into separate columns by your judgement, one for fusion, heating, and vaporization all against the same time x-axis. You can color code the three ranges differently to aid the reader.

• Use the trendlines to find dT/dt at ~2°C, ~50°C, and ~98°C.

  • dT/dt is the change in temperature over time, a higher value implies quicker change in temperature at that moment in time.

  • These temperatures are only a suggestion. You will want to choose a point in the fusion, heating, and vaporization ranges of the test.

• Calculate dQ/dt at each of 0-2°C, ~50°C, and ~98°C or the ranges you found from above.

  • dQ/dt is the change in heat over time, a higher value implies quicker transfer of sensible heat at that moment in time.

• Compare these result to the dW/dt for the element, which is equivalent to the electrical power measured by the Kill-A-Watt meter.

• How much energy was expected to be required to bring your sample to boiling given ideal conditions.

• How much energy was required to bring your sample to boiling ?

• Calculate the process efficiency by comparing the total energy used by the hot plate to that expected for your masses.

Questions

1. Explain the step-like appearance of the plot of temperature vs. time.

   • Comment on the rate of sensible vs latent heat transfer at each of the three temperatures.

2. How would you improve the efficiency of process? Make a recommendation based on techniques or equipment changes.