Answer
(a) $T = 9393.5^{\circ}C$
(b) $T = 693.5^{\circ}C$
Work Step by Step
(a) We can use Wien's law to find the temperature of the blackbody:
$\lambda = \frac{2.9\times 10^6~nm~K}{T}$
$T = \frac{2.9\times 10^6~nm~K}{\lambda}$
$T = \frac{2.9\times 10^{-3}~m~K}{300\times 10^{-9}~m}$
$T = 9666.7~K$
We can express the temperature in $^{\circ}C$:
$T = 9666.7-273.15 = 9393.5^{\circ}C$
(b) We can use Wien's law to find the temperature of the blackbody:
$\lambda = \frac{2.9\times 10^6~nm~K}{T}$
$T = \frac{2.9\times 10^6~nm~K}{\lambda}$
$T = \frac{2.9\times 10^{-3}~m~K}{3.00\times 10^{-6}~m}$
$T = 966.7~K$
We can express the temperature in $^{\circ}C$:
$T = 966.7-273.15 = 693.5^{\circ}C$
