Question

A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?

Short answer

We get the corresponding temperature in Fahrenheit is $4760°\mathrm{F}$and in Celcius is 2600℃.

Step-by-step solution

Relation between Kelvin and Fahrenheit scale

We can find Fahrenheit temperature from Kelvin temperature by the given equation,

$\mathbf{T}\left(°F\right)\mathbf{=}\frac{\mathbf{9}}{\mathbf{5}}\left[T\left(K\right)-273.15\right]\mathbf{+}\mathbf{32}$

Relation between Kelvin and Fahrenheit scale

The temperature in Kelvin is given,

$\mathbf{T}\left(K\right)\mathbf{=}\mathbf{2900}\mathbf{K}$

Adding this to the equation,

$$\begin{gathered} \mathbf{T}\left(°F\right)\mathbf{=}\frac{\mathbf{9}}{\mathbf{5}}\left(2900-273.15\right)\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\frac{\mathbf{9}}{\mathbf{5}}\mathbf{\times }\mathbf{2626}\mathbf{.}\mathbf{85}\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\mathbf{4728}\mathbf{.}\mathbf{33}\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\mathbf{4760}\mathbf{.}\mathbf{33} \end{gathered}$$

So. $\mathbf{4760}\mathbf{.}\mathbf{33}\mathbf{°}\mathbf{F}$is the Fahrenheit temperature equal to the Kelvin scale temperature of 2900 K.

Relation between Kelvin and Celcius scale

Kelvin scale related to Celcius scale temperature through the equation,

$\begin{array}{rcl}\mathbf{T}\left(°C\right)& \mathbf{=}& \mathbf{T}\left(K\right)\mathbf{-}\mathbf{273}\mathbf{.}\mathbf{15}\\ \mathbf{T}\left(°C\right)& \mathbf{=}& \mathbf{2900}\mathbf{-}\mathbf{273}\mathbf{.}\mathbf{15}\\ \mathbf{T}\left(°C\right)& \mathbf{=}& \mathbf{2626}\mathbf{.}\mathbf{85}\\ & & \end{array}$

So, the temperature on the Celcius scale is, or approximately equal to $\mathbf{2600}\mathbf{°}\mathit{C}$