Q4PE - College Physics (Urone)

Question

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

Step-by-Step Solution

Answer

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

Step 1: Relation between Kelvin and Fahrenheit scale

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

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

Step 1: 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.

Step 2: 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  $\mathbf{2600}\mathbf{°}\mathit{C}$