Scientists classify stars according to the following categories: O, B, A, F, G, K, M. A star's category depends upon its spectral type, which is determined by its temperature. The chart below shows five stars of different categories, along with their temperatures. $$ \begin{array}{|l|l|} \hline \text { Star Type } & \text { Temperature }\left({ }^{\circ} \mathbf{F}\right) \\ \hline \text { O } & 18,033 \\ \hline \text { B } & 9,978 \\ \hline \text { A } & 4,839 \\ \hline \text { F } & 3,644 \\ \hline \text { G } & 3,422 \\ \hline \end{array} $$ However, rather than measuring star temperature in degrees Fahrenheit, scientists typically measure star temperature in units of Kelvin. The conversion from Fahrenheit to Kelvin is given by the following formula: $$ \mathrm{K}=\frac{5}{9}\left({ }^{\circ} \mathrm{F}-32\right)+273 $$ What is the approximate temperature of the A-type star in Kelvin? You may use a calculator. A. 2,569 B. 2,822 C. 2,929 D. 2,944

Step by step solution

01

Identify the given information

First, let's identify the information given to us. We know an A-type star has a temperature of 4,839°F, and we have the formula to convert Fahrenheit to Kelvin: $$ K=\frac{5}{9}\left(^\circ F-32\right)+273 $$

02

Substitute the Fahrenheit temperature

Now, let's substitute the given temperature of the A-type star (4,839°F) into the formula for Kelvin: $$ K=\frac{5}{9}\left(4839-32\right)+273 $$

03

Calculation

Next, perform the required operations within the formula: $$ K=\frac{5}{9}\left(4807\right)+273 $$ Now, to calculate the fraction, divide 4807 by 9, and then multiply the result by 5: $$ K=5\left(533.0\right)+273 $$ Multiply 533.0 by 5: $$ K=2665+273 $$

04

Final calculation and answer

Add 2665 and 273 to get the final temperature in Kelvin: $$ K=2938 $$ Since the temperature is 2938 Kelvin, the closest approximate value from the given options is 2,944 Kelvin. Therefore, the correct answer is: D. 2,944

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