Q5PE - College Physics (Urone)

Question

The surface temperature of the Sun is about 5750 K. What is this temperature on the Fahrenheit scale?

Step-by-Step Solution

Answer

We get the temperature of the surface of the Sun in Fahrenheit as $9890°\mathrm{F}$ .

Step 1: Relation between Kelvin and Fahrenheit

Relations between the Kelvin scale and Fahrenheit scale are known. That is,

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

Step 2: Solution

The temperature in Kelvin is given by, 5750 K

Adding the value in the equation, we get,

$$\begin{gathered} \mathbf{T}\left(°F\right)\mathbf{=}\frac{\mathbf{9}}{\mathbf{5}}\left(5750-273.15\right)\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\frac{\mathbf{9}}{\mathbf{5}}\left(5476.85\right)\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\mathbf{9858}\mathbf{.}\mathbf{33}\mathbf{+}\mathbf{32} \\ \mathbf{T}\left(°F\right)\mathbf{=}\mathbf{9890}\mathbf{.}\mathbf{33}\mathbf{°}\mathbf{F} \\ \mathbf{T}\left(°F\right)\mathbf{=}\mathbf{9890}\mathbf{°}\mathbf{F} \end{gathered}$$

The temperature in Fahrenheit is  $\mathbf{9890}\mathbf{°}\mathit{F}$