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Convert 212 degrees Fahrenheit (F) to kelvin (K) - Junior Cycle Mathematics - Question 5 - 2015

Question 5

Convert 212 degrees Fahrenheit (F) to kelvin (K). Write an algebraic formula to express K in terms of F. Hence, or otherwise, convert 400 kelvin (K) to degrees Fah... show full transcript

Worked Solution & Example Answer:Convert 212 degrees Fahrenheit (F) to kelvin (K) - Junior Cycle Mathematics - Question 5 - 2015

Step 1

Convert 212 degrees Fahrenheit (F) to kelvin (K).

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Answer

To convert 212 degrees Fahrenheit to kelvin, we first apply the formula:

$K = \frac{(F + 459 - 67) \times 5}{9}$

Substituting in the value:

$K = \frac{(212 + 459 - 67) \times 5}{9}$

Calculating the inside:

$= \frac{(604) \times 5}{9}$

Calculating further gives:

$= \frac{3020}{9} \approx 335.56$

Thus, 212°F converts to approximately 373.15 K.

Step 2

Write an algebraic formula to express K in terms of F.

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Answer

The algebraic formula converting Fahrenheit (F) to kelvin (K) is:

$K = \frac{(F + 459 - 67) \times 5}{9}$

Step 3

Hence, or otherwise, convert 400 kelvin (K) to degrees Fahrenheit (F).

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Answer

To convert 400 K back to degrees Fahrenheit, we rearrange the formula:

Starting with:

$400 = \frac{(F + 459 - 67) \times 5}{9}$

Multiplying both sides by 9 gives:

$3600 = (F + 459 - 67) \times 5$

Dividing by 5 yields:

$720 = F + 459 - 67$

Now, simplifying gives:

$F = 720 + 67 - 459$

Thus, finally:

$F \approx 260.33$

Therefore, 400 K is approximately 260.33°F.

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