Question 1165498: The temperature in degrees Kelvin is 273 degrees more than the temperature in degrees Celsius. Use the formula C=5/9(F−32) to write a formula for the temperature in degrees Fahrenheit F in terms of the temperature in degrees Kelvin K.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! C = 5/9 * (F - 32) is the formula for converting fahrenheit temperature to celsius temperature.
fahrenheit freezing point is 32 degrees.
equivalent celsius freezing point is 5/9 * (F - 32) = 5/9 * 0 = 0.
fahrenheit boiling point is 212 degrees.
equivalent celsius boiling point is 5/9 * (212 - 32) = 5/9 * 180 = 100.
the kelvin temperature is given as always being 273 degrees more than the celsius temperature.
this means that K = C + 273.
solve for C to get C = K - 273.
in the formula of C = 5/9 * (F - 32), replace C with K - 273 to get:
K - 273 = 5/9 * (F - 32)
add 273 to both sides of this formula to get:
K = 5/9 * (F - 32) + 273.
that gives you the kelvin degrees in terms of fahrenheit degrees.
since we know that the boiling point in fahrenheit is 212 degrees, then the boiling point in kelvin degrees would be as shown below:
K = 5/9 * (212 - 32) + 273.
this gets you K = 373 degrees.
since we know that the boiling point in celsius degrees is 100, then the boiling point in kelvin is 273 degrees more than that.
this is consistent with the fact that kelvin degrees are always 273 degrees more than celsius degrees.
we know that the kelvin degrees in terms of fahrenheit degrees is equal to 5/9 * (F - 32) + 273.
to find the fahrenheit degrees in terms of kelvin degrees, we has to solve this equation for F.
start with K = 5/9 * (F - 32) + 273
subtract 273 from both sides of this equation to get:
K - 273 = 5/9 * (F - 32)
multiply both sides of this equation by 9/5 to get:
9/5 * (K - 273) = F - 32
add 32 to both sides of this formula to get:
9/5 * (K - 273) + 32 = F
the formula for F in terms of K becomes:
F = 9/5 * (K - 273) + 32
to see if this is true, let's look at freezing point in kelvin and boiling point in kelvin.
since kelvin is always 273 degrees more than celsius, we get:
freezing point of kelvin is 373 degrees and boiling point of kelvin is 373 degrees.
to find the freezing point in fahrenheit from the freezing point in kelvin, the formula becomes:
F = 9/5 * (273 - 273) + 32
this becomes F = 9/5 * 0 + 32 which becomes F = 32.
since we know this is the freezing point in fahrenheit, the formula is good for the freezing point in fahrenheit based on the freezing point in kelvin.
to find the boiling point in fahrenheit from the boiling point in kelvin, the formula becomes:
F = 9/5 * (373 - 273) + 32
this becomes F = 9/5 * 100 + 32 which becomes F = 180 + 32 which becomes f = 212.
since we know this is the boiling point in fahrenheit, the formula is good for the boiling point in fahrenheit based on the boiling point in kelvin.
your solution appears to be F = 9/5 * (K - 273) + 32
i think we could have arrived at this solution a little less painfully if we had done the following:
start with C = 5/9 * (F - 32)
multiply both sides of this formula to 9/5 to get:
9/5 * C = F - 32
add 32 to both sides of this equation to get:
9/5 * C + 32 = F
the formula for F in terms of C is therefore:
F = 9/5 * C + 32
the freezing point in centigrade is 0.
when C = 0, the formula becomes 9/5 * 0 + 32 = F which becomes 32 = F which is the freezing point in fahrenheit.
the boiling point in centigrade is 100.
when C = 100, the formula becomes 9/5 * 100 + 32 = 180 + 32 = 212 = F which is the boiling point in fahrenheit.
this confirms the formula for F from C is F = 9/5 * C + 32.
now we know that K is always 273 degrees more than C.
we get K = C + 273
solve for C to get C = K - 273
replace C with K - 273 in the formula of F = 9/5 * C + 32 and we get F = 9/5 * (K = 273) + 32
this is the same formula we got above with, i believe, a little less pain.
either way, that's your solution.
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