Radiation to T4. P=? A? T4 P?
Radiation is emitted from all objects above absolute zero; the rate of energy per unit area per unit time is proportional to T4. P=? A? T4 P? T4 P= power Watts ?= emissivity unit less constant related to the colour and reflectivity ?=Stephan’s constant Wm-2k-4 T=temperature Kelvin The peak wavelength of the radiation emitted can be calculated from Wein’s displacement law which states ? mT=2. 898×10-3 where ? m is the peak wavelength. I will be investigating Wein’s displacement law and the emissivity of a number of different surfaces. I will also be investigating how power affects temperature using Stefan’s power law.
Experiment 1 I will be using a computer program to simulate various temperatures and recording the peak wavelength (? m) that corresponds to a number of temperatures. I will then be plotting a graph of ? m against 1/T, the gradient of which should be 2. 898×10-3 mK. I will compare my results with Wein’s displacement law (see example below). Experiment 2 I will fill a cube with different emissivities on each side with boiling water and record the temperature it boils at as the pressure in the room will probably not be 1 atmosphere so the water will not boil at exactly 1000C.
I will record a reading of mV from a thermopile. As one of the sides is black, I will assume it is an ideal blackbody with an emissivity of 1. By then dividing the mV reading from the 3 other sides by this value, I will be able to determine their emissivity with mV/mV, giving a unit less constant as expected. Experiment 3 Stefan-Boltzmann lamp I will place the thermopile near a light bulb. I will then vary the power of the light bulb and record readings from the thermopile (P`) at various voltages from 1 to 12 with intervals of 1 volt.
From this I will be able to produce a graph which should show that P` varies with the fourth power of T. To do this I will plot a graph of lnP` against lnT. Temperature is related to the resistance of the bulb. I will calculate the temperature of the filament from a graph of RT/R300K against temperature (K), where R300K is 0. 5? i?? 0. 1, as room temperature in the lab is approximately 300 K and RT is calculated from V=IR. I will use insulating foam to shield the thermopile from the lamp and remove it when I open the shutter and record the volts.
I will do this 12 times using voltages from 1 to 12, increasing the volts by 1 each time. Between each recording, I will wait for the thermopile to return to room temperature. P`=K? A? T4 where K is a conversion factor as P`(mV) is not P (Watts) K? A? can be replaced with a new constant K` P`=K`T4 lnP`=ln(K`T4) lnP`=lnK`+ln(T4) lnP`=4ln(T)+lnK` Y=MX+C From the above equation it can be seen that the gradient of the graph should come out to be approximately 4. Results Temperature K 1/temp K-1 x10-6 ?m m.
Surface Reading mV Emissivity Black 7. 51 1. 0000 Dull 1. 83 0. 2437 Shiny 0. 77 0. 1025 Red 5. 67 0. 7550 I believe the uncertainly in the values of Emissivity due to the fact that the black side is not an ideal black body and the error in the readings from the thermopile to be about i?? 0. 05 in the values of Emissivity T K P.
Conclusion The gradient of the graph was 4. 14 this means that the power increases with the 4 power of T this is a good indication the experiment was successful and the readings were accurate as it follows the original equation P=? A? T4 P? T4. from the weins displacement law experiment the vale of the constant cam out to be 3. 44×10-3 this is not as close as expected this is probably due to errors in interrupting the data from the computer program.