Problem of the day! (Thermodynamics)

in #ocd8 months ago

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.

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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)