Question

The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of:

• A. -40°F
• B. 313°F
• C. 574.6°F
• D. 732.7°F

Answer 1

Answer: (C)

574.6°F

Answer 2

The correct option is: (C) : 574.6°F.

To find the temperature at which the Fahrenheit and Kelvin scales have the same reading, we can use the conversion formulas between Fahrenheit (F) and Kelvin (K) temperatures:

F = (9/5)K - 459.67

Where F is the temperature in Fahrenheit and K is the temperature in Kelvin.

Setting the two scales equal to each other:

(9/5)K - 459.67 = K

Now, solve for K:

(9/5)K - K = 459.67

Simplify the equation:

(9/5 - 1)K = 459.67

(4/5)K = 459.67

Now, solve for K:

K = (5/4) * 459.67 ≈ 574.5875

So, at a temperature of approximately 574.5875 Kelvin, the Fahrenheit and Kelvin scales will have the same reading.

Now, convert this temperature to Fahrenheit using the conversion formula:

F = (9/5)K - 459.67

F = (9/5) * 574.5875 - 459.67 ≈ 574.6°F