Q4PE - College Physics (Urone)

Question

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

Answer

We get the corresponding temperature in Fahrenheit is 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,

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

 T(K)=2900K

Adding this to the equation, 

 $$\begin{gathered} T(°F)=\frac{9}{5}(2900-273.15)+32 \\ T(°F)=\frac{9}{5}\times 2626.85+32 \\ T(°F)=4728.33+32 \\ T(°F)=4760.33 \end{gathered}$$

So. 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,

 $$\begin{gathered} T(°C)=T\left(K\right)-273.15 \\ T(°C)=2900-273.15 \\ T(°C)=2626.85 \end{gathered}$$

So, the temperature on the Celcius scale is, or approximately equal to  2600⁰C