4. Heat and Thermal Energy

Transcription

1 4. Heat and Thermal Energy Introduction The purpose of this experiment is to study cooling and heating by conduction, convection, and radiation. Thermal energy is the energy of random molecular motion. Heat is thermal energy transferred. If heat Q is added or removed from an object, then the temperature of the object changes. The heat added or removed Q and the change in temperature ΔT are related by: Q = mcδt (J) (1) where m and c are the mass and specific heat of the substance. Heat Q is transferred by conduction, convection, or radiation. The rate of transferring energy by conduction is given by: Q ΔT P = = ka (J/s) or (W) (2) Δt L where k, A, and L are the thermal conductivity, the cross-sectional area, and the length or thickness. In the figure T > T o. L A T T 0 Q The rate of transferring energy by radiation is given by: P = σae(t 4 T e 4 ) (W) (3) where σ is a constant, A is the surface area of the object, e is the emissivity of the surface (o<e<1), T is the surface temperature of the object in kelvins, and T e is the temperature of the enviroment. There is no simple equation that describes heat transfer by convection. 29

2 Objectives To become familiar with the different mechanisms of heat transfer. To verify the law of conservation of energy. To learn to calculate and measure the amount of energy needed to raise the temperature of different substances. To review methods of graphically analyzing non-linear data sets. Prelab Questions 1. How does heat transfer by conduction change if the thickness L is changed? In particular, if the thickness of object is doubled, then the rate of heat transfer by conduction will by a factor of. 2. How does the power radiated by an object change if the temperature T of the radiating object changes? Here we ignore the surroundings at temperature T e. In particular, if T is halved, then the power radiated by a factor of. 3. The star Betelguese has a radius and surface temperature of about 10 8 miles and 3000 K. The sun has a radius and surface temperature of about miles and 6000 K. The ratio of the power radiated by the sun and Betelguese, P Sun / P Bet, is. Assume the emissivity of the stars is the same. The surface area of a sphere is A = 4πr 2. Cooling by Conduction In this part of the lab you will measure the temperature of a canister of water as it cools primarily through conduction. Computer setup 1. Connect the Data Studio interface to the computer, turn on the interface, and then turn on the computer. 2. Double click on the Data Studio icon. When the window opens click on Create Experiment. 3. Plug the Temperature Sensor into Analog Channel A 4. In the Sensors panel on the left, scroll down to Temperature Sensor and double click. An icon for the temperature sensor will appear in the right panel. 5. Create a Temperature graph. 30

3 Data collection 1. The apparatus, shown below, is a nested set of canisters. Remove the inner canister and fill the larger canister to the line marked inside with tap water. Insert the temperature sensor into the lid such that the end of the sensor reaches about the middle of the smaller canister. Place the smaller canister with its supporting ring inside the larger canister. It will float. Carefully fill the smaller canister with boiling water and place the lid on the system. 2. To record the temperature, double click on Start. Stir continuously during the cooling process. After about 400 s click on Stop. Print the graph for your notebook. Stirrer Temp sensor Interface Digital Analog computer Inner canister Question 1. From your graph, when the system was cooling did it cool faster at the beginning of the experiment or toward the end of the experiment? Is this what you would expect from equation (2)? Explain. Heating In this part of the experiment electrical energy is converted to thermal energy. You will measure the energy dissipated by a metal coil in a canister of water and compare it to the change in the water s thermal energy. The apparatus you will use is shown below. To Interface Power Supply Stirrer Heater Temp sensor 31

4 Data Collection 1. Empty the water from both the outer and inner canisters. Weigh the inner canister, and then add 200 ml of cold tap water to the small canister and again weigh the canister with the water in it. Record the mass of the canister (m c ) and the mass of water (m w ) in kg. 2. Place the small canister inside the empty larger one. Position the end of the temperature sensor in the middle of the small canister. 3. Set up the computer so that a Graph of temperature vs. time is on the screen, and set the Maximum and Minimum times to 400 and 0 seconds. Double click on Digits in the lower left corner of the screen to create a numerical readout of the temperature. Start recording data, and record the initial temperature (T i ) in your notebook. Turn on the power supply and set the voltage to 10.0 V. 4. Record the voltage (V) and current (I) from the power supply. Continue to stir the water while the power supply is on. 5. After about 300 s turn off the power supply and click Stop. Measure Δt from your graph and measure the final temperature (T f ) from the digital meter. Calculate the change in temperature of the water ΔT = T f T i. Data Analysis 6. First skip ahead to the section Cooling by Radiation and Convection and start the experiment. While the computer is collecting data you can analyse this data. 7. The electrical power is the current I in amperes (A) times the voltage in volts (V). The electrical energy dissipated during time Δt is: E = IVΔt (Joules) (4) Calculate how much energy was produced by the power supply while you were heating the water. 8. The heat input to the water during that time is: Q = m w c w ΔT + m c c c ΔT (Joules) (5) where the specific heats are c w = 4,186 J/kg C and c c = 900 J/kg C. This takes into account the energy needed to heat the water plus the energy needed to heat the canister. With your data calculate how much energy was used to heat the water and canister by ΔT. Question 2. Was the heat Q transferred to the water greater or less than the energy E dissipated by the resistive wire? Explain why you might expect there to be a discrepancy between these two 32

5 values. Calculate the % discrepency between the heat input to the water and the electrical energy dissipated. Cooling by Radiation and Convection Newton s law of cooling states that the rate at which an object cools in proportional to the difference between its temperature and the surrounding temperature. That is the temperature T will decreases exponentially with time t: ct ( t) = ( T Te ) e Te T 0 + (6) where c is a constant with units of 1/sec, T 0 is the objects initial temperature, and T e is the temperature of the enviroment. In this part of the lab you will test to see if cooling by radiation and convection obey Newton s law of cooling. 1. Set up the computer so that a Graph of temperature vs. time is on the screen, and set the Maximum and Minimum times to 20 and 0 minutes. 2. Carefully fill the black can about 2/3 full with hot water. Replace the lid and insert the thermistor into the center of the can. 3. Wait 5 minutes for the temperature of the can and water to come to equilibrium. Then start recording the temperature as a function of time. 4. Take data for at least 20 minutes and then click Stop. Print the graph for your notebook. Question 3. Does Newton s law of cooling appear to be satisfied? 4. Answering question 3 based on this graph alone can be challenging. A much better option would be to create a semilog plot like we did in the last experiment. In order to do this export your data as a text file (Display Export Data), then open this file with excel. You should have two collumns of data: time and temperature. Subtract room temperature (T e ) from your temperature data and take the natural log of this difference and plot this as a function of time. Based on equation (6) what should your graph look like? Find the equation of the best-fit line and again answer question 3. What is the constant c for your system? Print out this graph and add it to your notenbook. 33