Problem of the day! (Thermodynamics)
Derivation of the following temperatures formula:
Fahrenheit to Celsius
Celsius to Fahrenheit;
Fahrenheit to Kelvin
Kelvin to Fahrenheit
Celsius to Kelvin
Kelvin to Celsius
Fahrenheit to Rankine
Rankine to Fahrenheit
Celsius to Rankine
Rankine to Celsius
Solution:
Let;
Temperature in Celsius equal to TC
Temperature in Fahrenheit equal to TF
Temperature in Kelvin equal to TK
Temperature in Rankine equal to TR
So, based from the illustration below.
using interpolation method;
TF to TC
a/b = c/d
where; a = TC – 0; b = 100 – 0; c = TF – 32; d = 212 – 32
(TC-0)/(100-0) = (TF-32)/(212-32)
TC/100 = (TF-32)/180
(TC)(180)/100 = TF -32
TF = [(TC)(180)/100] + 32
TF = 9/5(TC) + 32 (conversion from Fahrenheit to Celsius)
TC to TF
TF = 9/5(TC) + 32
9/5(TC) = TF – 32
**TC = 5/9(TF-32) (conversion from Celsius to Fahrenheit) **
TF to TK
c/d = e/f
where; c = TF – 32; d = 212 – 32; e = TK – 273; f = 373 – 273
(TF-32)/(212-32) = (TK-273)/(373-273)
(TF-32)/(180) = (TK-273)/(100)
TF-32 = (TK-273)(180)/100
TF-32 = 9/5(TK-273)
**TF = 9/5(TK-273) + 32 (conversion from Fahrenheit to Kelvin) **
TK to TF
TF = 9/5(TK-273) + 32
9/5(TK-273) = TF-32
TK-273 = 5/9(TF-32)
TK = 5/9(TF-32) + 273 (conversion from Kelvin to Fahrenheit)
TC to TK
a/b = e/f
where; a = TC – 0; b = 100 – 0; e = TK – 273; f = 373 – 273
(TC-0)/(100-0) = (TK-273)/(373-273)
TC/100 = (TK-273)/(100)
**TC = TK-273 (conversion from Celsius to Kelvin) **
TK to TC
TC = TK-273
TK = TC+273 (conversion from Kelvin to Celsius)
TF to TR
c/d = g/h
Where; c = TF – 32; d = 212 – 32; g = TR – 492; h = 672 – 492
(TF-32)/(212-32) = (TR-492)/(672-492)
(TF-32)/180 = (TR-492)/180
TF-32 = TR-492
TF = TR – 492 +32
**TF = TR – 460 (conversion from Fahrenheit to Rankine) **
TR to TF
TF = TR – 460
**TR = TF + 460 (conversion from Rankine to Fahrenheit) **
TC to TR
a/b = g/h
Where; a = TC – 0; b = 100 – 0; g = TR – 492; h = 672 – 492
(TC-0)/(100-0) = (TR-492)/(672-492)
TC/100 = (TR-492)/180
TC = (TR-492)(100)/180
**TC = 5/9(TR-492) (conversion from Celsius to Rankine) **
TR to TC
TC = 5/9(TR-492)
TC(9/5) = TR-492
TR = 9/5(TC) + 492 (conversion from Rankine to Celsius)