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Found in: Page 470

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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

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

See the step by step solution

## 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,

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

${\mathbf{T}}\left(°F\right){\mathbf{=}}\frac{\mathbf{9}}{\mathbf{5}}\left(2900-273.15\right){\mathbf{+}}{\mathbf{32}}\phantom{\rule{0ex}{0ex}}{\mathbf{T}}\left(°F\right){\mathbf{=}}\frac{\mathbf{9}}{\mathbf{5}}{\mathbf{×}}{\mathbf{2626}}{\mathbf{.}}{\mathbf{85}}{\mathbf{+}}{\mathbf{32}}\phantom{\rule{0ex}{0ex}}{\mathbf{T}}\left(°F\right){\mathbf{=}}{\mathbf{4728}}{\mathbf{.}}{\mathbf{33}}{\mathbf{+}}{\mathbf{32}}\phantom{\rule{0ex}{0ex}}{\mathbf{T}}\left(°F\right){\mathbf{=}}{\mathbf{4760}}{\mathbf{.}}{\mathbf{33}}$

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 ${\mathbf{2600}}{\mathbf{°}}{\mathbit{C}}$