Lab / experiment Grade 12 Science
Thermal Plume Mixing at the Kelverne Station Outfall
A grade 12 science lab in which students mix warm and cool water at three ratios, predict each final temperature with an energy balance, and test the prediction.
Objectives
- Students will predict the final temperature of a mixture using a volume-weighted energy balance.
- Students will compare predicted and measured temperatures across three dilution ratios.
- Students will connect a modeled temperature rise to a stated mixing-zone limit and to dissolved oxygen.
Vocabulary
- Dissolved oxygen
- Dissolved oxygen is the oxygen gas mixed into water that fish and other underwater animals breathe. Cold, moving water holds more oxygen than warm, still water.
Also: thermal pollution, mixing zone, energy balance, dilution ratio, thermal equilibrium
Teacher overview
The fictional Kelverne Station draws cooling water from the Vessey River and returns it several degrees warmer. Permits for discharges like this one limit how much the river may be warmed at the edge of a defined mixing zone, because warm water holds less dissolved oxygen and most fish need dissolved oxygen above 5 mg/L. The investigation question for this lab is whether a simple volume-weighted energy balance predicts the temperature that results when warm discharge water joins cooler river water, and how the prediction holds up as dilution increases.
Students model the outfall at three dilution ratios using tap water, predict each result before measuring it, and then compare the two. The classroom mixture is an analog, not a measurement of any real river, and the containers used here lose heat to the room in ways a river does not.
Procedure
Step 1. Safety: keep the hot water below 50 degrees Celsius, carry containers with both hands, wipe spills immediately because wet floors are the main hazard in this lab, and do not drink any sample. Report broken glass to your teacher rather than picking it up.
Step 2. Label three containers A, B, and C. Container A is the 1 part warm to 1 part cool trial, container B is 1 to 3, and container C is 1 to 9.
Step 3. Collect warm water in one insulated container and cool water in another. Record the temperature of each to the finest division your thermometer allows. Take these readings immediately before mixing, since both will drift toward room temperature.
Step 4. Before mixing anything, calculate a predicted final temperature for each of the three trials using the volume-weighted energy balance below, and write the three predictions in the data table. Predicting first is what makes the comparison meaningful.
Predicted final temperature = (warm volume x warm temperature + cool volume x cool temperature) / (warm volume + cool volume)
Step 5. Trial A: measure 100 mL of cool water into container A, then add 100 mL of warm water. Stir for ten seconds, then read the temperature within fifteen seconds of mixing and record it.
Step 6. Trial B: measure 150 mL of cool water into container B, then add 50 mL of warm water. Stir for ten seconds and read as before.
Step 7. Trial C: measure 360 mL of cool water into container C, then add 40 mL of warm water. Stir for ten seconds and read as before.
Step 8. Re-measure the temperature of the warm and cool source water, then repeat all three trials as a second set. Use the fresh source temperatures for the second set of predictions rather than the ones recorded in step 3.
Step 9. Empty the containers, dry the thermometers, and return all equipment. Record the room temperature before you leave, since you will use it when you discuss sources of error.
Data & Analysis
Record both sets of trials.
| Trial | Warm volume (mL) | Warm temp (C) | Cool volume (mL) | Cool temp (C) | Predicted final (C) | Measured final (C) | Measured minus predicted (C) |
|---|---|---|---|---|---|---|---|
| A, set 1 | 100 | 100 | |||||
| B, set 1 | 50 | 150 | |||||
| C, set 1 | 40 | 360 | |||||
| A, set 2 | 100 | 100 | |||||
| B, set 2 | 50 | 150 | |||||
| C, set 2 | 40 | 360 |
Write out the full substitution into the energy balance for your trial A, set 1, and give the predicted final temperature you obtained.
Report the difference between your measured and predicted final temperature for trial A, set 1, in degrees Celsius, and state whether the measurement came in above or below the prediction.
Rank your three set-1 trials by how far the final temperature rose above the cool-water starting temperature, from largest rise to smallest, and state the pattern the ranking shows.
Another class recorded 40 mL of warm water at 46.0 degrees Celsius poured into 360 mL of cool water at 14.0 degrees Celsius. Calculate the predicted final temperature for that mixture. Round to one decimal place.
Using that same class data, calculate how many degrees above the 14.0-degree starting temperature the mixture ends up. Round to one decimal place.
The fictional permit for the Kelverne Station allows a rise of no more than 2.8 degrees Celsius at the edge of the mixing zone. Does the mixture in question 4 meet that limit? Answer yes or no.
Using the same 40 mL of 46.0-degree discharge water, calculate the volume of 14.0-degree cool water needed to hold the rise to exactly 2.8 degrees Celsius. Round to the nearest milliliter.
Warm water holds less dissolved gas than cool water. Explain how a rise of the size you calculated in question 5 could move a summer stream toward the 5 mg/L dissolved oxygen benchmark most fish need.
Name one source of error in your procedure, state whether it would push your measured final temperature above or below the prediction, and explain the reasoning.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: Accept any correct substitution matching the group's own recorded volumes and temperatures.
A correct response shows the numerator as 100 times the warm temperature plus 100 times the cool temperature, and the denominator as 200. With equal volumes the prediction is simply the average of the two starting temperatures, so a group starting at 44.0 and 16.0 degrees should predict 30.0 degrees. Look for correct units and a result that falls between the two starting temperatures.Answer: Accept any value, typically 0.2 to 1.5 degrees Celsius below the prediction.
Measured values almost always fall short of the prediction because heat leaves to the room, the containers, and the thermometer itself. A measurement above the prediction usually means a source temperature was recorded too low, for example a cool-water reading taken well before mixing, while the cool water was still warming toward room temperature, or a warm-water reading taken before the thermometer had fully warmed. Students should state the direction, not only the size, of the difference.Answer: Trial A shows the largest rise, then B, then C.
The rise above the cool-water temperature scales with the fraction of warm water in the mixture: one half in trial A, one quarter in trial B, and one tenth in trial C. The pattern to name is that increasing dilution reduces the temperature rise proportionally, which is the same reason a permit is written around the flow available for mixing.Answer: 17.2 degrees Celsius.
(40 x 46.0) + (360 x 14.0) = 1,840 + 5,040 = 6,880. Dividing by the total volume: 6,880 / 400 = 17.2 degrees Celsius.Answer: 3.2 degrees Celsius.
17.2 - 14.0 = 3.2 degrees Celsius above the starting temperature of the cool water.Answer: No.
A rise of 3.2 degrees exceeds the 2.8-degree limit, so this mixture would not meet the stated permit condition at the edge of the mixing zone.Answer: 417 mL of cool water.
The rise equals the warm fraction times the 32.0-degree temperature difference. Setting that equal to the limit: fraction x 32.0 = 2.8, so the warm fraction must be 2.8 / 32.0 = 0.0875. With 40 mL of warm water, the total volume must be 40 / 0.0875 = 457.1 mL, so the cool water needed is 457.1 - 40 = 417.1 mL, which rounds to 417 mL. That is roughly one part discharge to ten and a half parts river water.Answer: The warmer water holds less oxygen at saturation, so the same stream carries less dissolved oxygen after mixing.
Accept responses that make two moves. First, oxygen solubility falls as temperature rises, so a stream already near its summer maximum temperature loses capacity with every added degree. Second, warmer water also speeds up the respiration of fish and of the microbes decomposing organic matter, so demand for oxygen rises at the same time the supply falls. A stream sitting just above the 5 mg/L benchmark can cross below it from a rise of a few degrees, and the fish that need the most oxygen are affected first.Answer: Accept any identified source of error with a stated direction and a sound reason.
Common valid answers include heat lost to the room and the container, which pushes the measured value below the prediction; a thermometer left in the cool water long enough to warm it before the reading, which raises the recorded cool temperature; a delay between mixing and reading, which lowers the measured value; and imprecise volume measurement in the graduated cylinder, which can shift the result either direction. The response must state the direction and connect it to the physical cause, not just name the error.
Differentiation
Support
Give students the energy-balance equation with the warm and cool terms already labeled on a diagram of the fictional Kelverne outfall, and complete the trial A prediction together as a class before groups move to trials B and C. Provide a partially filled data table with the volumes entered and only the temperature columns blank. For questions 4 through 7, supply a worked example using different numbers so the sequence of prediction, rise, and comparison is modeled first.
Extension
Have groups add a fourth trial at one part warm to nineteen parts cool, predict the rise before measuring, and explain why the difference between predicted and measured values becomes harder to detect as dilution increases. Ask them to estimate the smallest temperature rise their thermometer could reliably detect and to state what that resolution implies about verifying compliance with a 2.8-degree limit in a real river.
ELL supports
Provide a labeled diagram of the fictional discharge and mixing zone with arrows for warm water in, river water in, and mixed water out, and place the six vocabulary terms on the diagram. Give sentence frames for questions 3, 8, and 9, such as "As the amount of cool water increases, the temperature rise ___ because ___." Allow groups to record their trial procedure as a numbered picture sequence before writing.
Extensions
Groups can repeat trial C using an insulated cup and a foam lid, then compare the predicted-versus-measured difference against their uninsulated result and explain what the change reveals about where the missing heat went in the original setup. A second option is to have students find a published table of oxygen solubility in fresh water, read the values for the two temperatures in question 4, and calculate how much dissolved oxygen capacity the fictional mixture lost.