Question

the tip of a cigarette often becomes
ed hot\ when a smoker inhales. using the relation between dominant wavelength and temperature for an ideal radiator, estimate the cigarette tip temperature knowing that red color has a wavelength of about 0.65 micrometer. a. 2900 k b. 4500 k c. 6500 k d. 3400 l

Explanation:

Step1: Use Wien's displacement law

Wien's displacement law is given by \(\lambda_{m}T = b\), where \(b = 2.9\times10^{-3}\text{m}\cdot\text{K}\) (Wien's constant), \(\lambda_{m}\) is the wavelength of maximum intensity and \(T\) is the temperature.

Step2: Rearrange the formula to solve for \(T\)

We can rewrite the formula as \(T=\frac{b}{\lambda_{m}}\). Given \(\lambda_{m}=0.65\times 10^{- 6}\text{m}\) (since \(1\) micrometer \( = 10^{-6}\text{m}\)).
Substitute \(b = 2.9\times10^{-3}\text{m}\cdot\text{K}\) and \(\lambda_{m}=0.65\times 10^{-6}\text{m}\) into the formula:
\(T=\frac{2.9\times 10^{-3}}{0.65\times 10^{-6}}\)

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Answer:

b. \(4500\) K