Use Newton s law of cooling to narrow down the number of suspects by determining when the victim was killed.

Transcription

1 Case File 14 Hot Air, Cold Body: Using Newton s law of cooling to determine time of death Use Newton s law of cooling to narrow down the number of suspects by determining when the victim was killed. Memo to Detective Sergeant: The elevator operator of the Ritz Palace Hotel died from a stab wound while on duty last Thursday evening. His body was discovered by a family on its way down to the pool. When we arrived at the scene, we canvassed the area but found nothing. The elevator is full of fingerprints of the hundreds of guests who ride it during the day. We have several suspects in mind, but we are having trouble pinning down the time of death. If we can determine that, we have a good shot at finding the killer. Enclosed are a photograph of the crime scene and part of the paramedic report Paramedic report Date: 10/5/05 Time: 9:45 p.m. Evaluation copy Body temperature: 26ºC Notes: Elevator temperature was 20ºC

2 Hot Air, Cold Body Case 14 OBJECTIVE Determine the time of death of a person who has died within the last few hours. Create a temperature vs. time graph for cooling. Model the temperature data with an exponential function. Use the model to estimate time of death. MATERIALS computer ring stand with clamp Vernier computer interface test tube and test tube rack Logger Pro water at 50 C Vernier Temperature Probe PROCEDURE 1. Use the paramedic report to record the body temperature in the Evidence Record. Also enter the time that the body temperature was measured. Part I: Collecting Data to Model the Cooling of the Body 2. Connect the Temperature Probe to the computer interface. Prepare the computer for data collection by opening the file 14 Hot Air, Cold Body from the Forensics with Vernier folder of Logger Pro. 3. Determine room temperature in the lab. a. Hold the Temperature Probe in the air away from heat sources and sunlight. Make sure the tip of the probe is not touching anything warmer or cooler than room temperature (such as your hand). b. Record the room temperature in your Evidence Record. 4. Attach Temperature Probe to the clamp. Add 20 ml of the 50 C water to the test tube and place the test tube in the test tube rack. Place the temperature probe in the water with the probe near the center of the test tube and away from the side of the test tube. 5. Wait for the temperature sensor to reach the temperature of the water. Click to begin data collection. Evaluation copy Part II: Modeling the Data with an Exponential Function 6. Newton s law of cooling is an exponential relationship that states T = T 0 e kt + T room where T is temperature of the object at any time t, T 0 represents the initial temperature difference between the initial temperature of the object and the room temperature, k is a constant that represents the cooling rate, and T room is the room temperature. Forensics with Vernier 14-1

3 Case Use Logger Pro to fit an exponential function to the data. a. Click once on your graph to make it active. b. Select Curve Fit from the Analyze menu. c. Choose Natural Exponential (y = A*exp(-Ct)+B) from the General Equation list. d. Click to display the exponential fit on the main graph. The equation for the curve fit is displayed in a floating box. e. Enter the values for A, B and C in the Evidence Record. 8. The fitted curve represents a model that predicts what the temperature of the body will be as it cools to room temperature. The Logger Pro graph is scaled to show this model to when the sample will approach room temperature. You will examine the fitted curve to estimate the time that it would take your sample to cool to 26 C. a. Choose Interpolate from the Analyze menu. b. Click the Examine button. Move the mouse to the point where the temperature is 37 C (body temperature). Record the time in minutes in the Evidence Record. c. Move the mouse to the point where the temperature is 26 C. Record the time in minutes in the Evidence Record. d. Calculate the elapsed time and record it in the Evidence Record. EVIDENCE RECORD Temperature of body (ºC) Time body temperature was measured Modeling the cooling in the lab Ambient (room) temperature in the lab (ºC) Variables from the fitted curve A C B Temperatures and times from the fitted curve Time that the water was at 37ºC (minutes) Time that the water was at 26ºC (minutes) Elapsed time (minutes) 14-2 Forensics with Vernier

4 CASE ANALYSIS Hot Air, Cold Body 1. Match the variables A, B, and C in the fitted equation to the terms T 0, k, and T room, in the expression of Newton s law of cooling. From Newton s law of cooling T 0 Cooling constant, k T room 2. The term T room represents the room temperature. How closely does this term match the room temperature in the lab experiment? 3. The T 0 term represents that initial difference between the water temperature and the room temperature. How closely does this term match your data? 4. Use the elapsed time for your sample to cool to 26ºC to estimate the time of death in the case. 5. The experiment performed to model the cooling of a victim is much simpler than the actual cooling at a crime scene. What other facts would affect the cooling rate of a victim? Forensics with Vernier 14-3

5 Vernier Lab Safety Instructions Disclaimer THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB. This copy does not include: Safety information Essential instructor background information Directions for preparing solutions Important tips for successfully doing these labs The complete Forensics with Vernier lab manual includes 14 labs and essential teacher information. The full lab book is available for purchase at: Vernier Software & Technology S.W. Millikan Way Beaverton, OR Toll Free (888) (503) FAX (503)