Modelling dynamical equilibrium in emission and absorption of radiation

1. Modelling dynamical equilibrium in emission and absorption of radiation Why a black and a white can may be so interesting? Daniela Allasia and Giuseppina Rinaudo Experimental Physics Dept. – University of Torino – http://www.iapht.unito.it/ GIREP Conference – Amsterdam – August 21-25, 2006

2. The experiment We all know that the temperature of a black object rises faster than that of a white object when exposed to radiation. The questions are: • How much faster? • Does the black object also cool faster, as expected from Kirchof law? • How is the dynamical equilibrium reached during heating? D. Allasia, G. Rinaudo - GIREP Conference – Amsterdam – August 21-25, 2006

3. temperature sensors for manual readout graphic calculator and ADC converter temperature sensors for online readout hot filament bulb lamp The experimental setup D. Allasia, G. Rinaudo - GIREP Conference – Amsterdam – August 21-25, 2006

4. “dynamical” equilibrium black can white can lamp is turned off “static” equilibrium Black and white cans: heating by radiation and cooling D. Allasia, G. Rinaudo - GIREP Conference – Amsterdam – August 21-25, 2006

5. Temperature differences from equilibrium values in log scale black black white white Heating T = Tdyn.eq-T Cooling T = T- Tstatic.eq

6. Heating Cooling Results -The black and the white cans reach the dynamical equilibrium temperatures when they are heated by the lamp with characteristic times dwhich are close to the times sat which they reach the static equilibrium temperature when they cool down: the characteristic times seem thus to be independent from the presence or the power of the radiation source • The characteristic times dand sof theblack can are much smaller than those of the white can and indicate a stronger coupling with the environment • The dynamical equilibrium temperature of theblack can is larger than that of the white can and depends on the power of the source • Also the static equilibrium temperature of theblack can is slightly larger than that of the white can

7. Rate of temperature variation Model for cooling Model for heating black white

8. heating black white cooling The temperature variation rate vs. temperature Cooling Heating white The relation is linear; the slope is 1/ black black

9. Results of the fit • The characteristic “dynamical relaxation time” dwhile heating is close to the “static relaxation time” swhile cooling both for the white and the black cans • The characteristic times of the white can are longer than those of the black can • The dynamical and static equilibrium temperatures of the black can are larger than those of the white can

10. Final question Is the “static equilibrium temperature” (room temperature) seen by the black can really higher than that seen by the white can? • The effect is real: • the “room temperature” may be different in the same place when seen by different sensors! • The black can behaves as a “radiometer”, being • more sensitive (higher equilibrium temperature) • more responsive (smaller characteristic time) to the IR radiation and to its direction

11. black painted metal strips 20.5 °C 20.9 °C white painted metal strips A “home made” radiometer The two identical black strips detect different temperatures in the opposite directions even without an apparent source of radiation