Question 40.1: How hot is that flame? We normally associate the color blue ......
How hot is that flame?
We normally associate the color blue with cold objects and the color red with hot ones, but this association probably arises from our thinking of water as blue and cool and fire as red and hot. In reality, a blue black body is hotter than a red one. Take a close look at the flame in Figure 40.7, and you will see the flame is blue near the source and red on the far end. Model the flame as a black body, and estimate the temperature at each end. In the check and think step, consider that a candle’s flame has a temperature of about 1000°C.
INTERPRET and ANTICIPATE
We expect to get a higher temperature for the blue part of the flame.
SOLVE
From the photos and Figure 34.11 (page 1101), we estimate the wavelengths based on the color of each flame. (It is okay to keep an extra significant figure for this step.)
Blue: \lambda_{blue} = 475 nm
Red: \lambda_{red} = 675 nm
Assume that the observed color is near the peak of the black-body spectrum for each flame; then the temperature can be estimated from Wien’s law. Our estimates are only good to two significant figures.
\begin{gathered}\lambda_{\max } T=2.898 \times 10^6 nm \cdot K \quad \quad (40.1)\\ T=\frac{2.898 \times 10^6 nm \cdot K }{\lambda_{\max }}\\\end{gathered} \begin{aligned} \text{Blue} : & T_{\text {blue }}=\frac{2.898 \times 10^6 nm \cdot K }{475 nm } \approx 6.1 \times 10^3 K \\ \text{Red}: & T_{\text {red }}=\frac{2.898 \times 10^6 nm \cdot K }{675 nm } \approx 4.3 \times 10^3 K \end{aligned}CHECK AND THINK
We found that the blue part is hotter than the red part. This result is satisfying because the blue part is closer to the source, and we expect the flame to be hotter near the source. However, there must be something wrong because the temperatures we found (about 5000°C) are considerably greater than the 1000°C we were expecting for a candle’s flame. The problem is that we assumed the flame could be modeled as a black body, but a candle’s flame is more complicated than a simple black body. The color (and temperature) variation depends on the chemical reactions that occur in various parts of the flame. In Section 42-3, we see how the structure of atoms affects the radiation we observe; not all radiation is well-modeled as black body radiation.
