MATH for SCIENCEMATH for SCIENCE

Temperature ConversionsTemperature Conversions

I.I. Temperature Scales ~Temperature Scales ~

There are three different temperature scales; Fahrenheit, Celsius, and There are three different temperature scales; Fahrenheit, Celsius, and Kelvin. Kelvin.

A.A. In the United States the Fahrenheit scale is used to measure the In the United States the Fahrenheit scale is used to measure the

environmental temperatures. environmental temperatures.

B.B. Most other nations use the Celsius scale for environmental Most other nations use the Celsius scale for environmental

temperaturestemperatures..C.C. The Standard International (SI) temperature scale used in science The Standard International (SI) temperature scale used in science is is

the Kelvin scale.the Kelvin scale.

II.II. Conversion Formulas ~Conversion Formulas ~

A.A. Fahrenheit to CelsiusFahrenheit to Celsius C.C. Celsius to KelvinCelsius to KelvinooC = C = 55 ( (ooF – 32F – 32oo)) ooC = C = ooK – 273K – 273oo

99B.B. Celsius to FahrenheitCelsius to Fahrenheit D.D. Kelvin to CelsiusKelvin to Celsius

ooF = F = 99 ooC + 32C + 32oo ooK = K = ooC + 273C + 273oo

55E.E. Fahrenheit to KelvinFahrenheit to Kelvin F.F. Kelvin to FahrenheitKelvin to Fahrenheit

This is a two step process.This is a two step process. This is a two step process.This is a two step process.Step 1. Step 1. ooC = C = 55((ooF – 32)F – 32) Step 1. Step 1. ooC = C = ooK – 273K – 273

99 Step 2. Step 2. ooK = K = ooC + 273C + 273 Step 2. Step 2. ooF = F = 99ooC + 32C + 32

55

III.III. Water ScalesWater Scales

The temperatures for when water freezes and boils differ according to the The temperatures for when water freezes and boils differ according to the temperature scale being used. See the following chart:temperature scale being used. See the following chart:

At sea level & 25 At sea level & 25 ooCC FahrenheitFahrenheit Celsius Celsius KelvinKelvin

Water BoilingWater Boiling 212 212oo F F 100 100oo C C 373373oo K K

Water FreezingWater Freezing 32 32oo F F 0 0oo C C 273 273oo K K

IV.IV. Conversion Problems ~ Conversion Problems ~

These temperature conversion problems are easily done by substituting the These temperature conversion problems are easily done by substituting the given temperature into the appropriate equation. given temperature into the appropriate equation.

A. Fahrenheit to CelsiusA. Fahrenheit to Celsius ooC = C = 55 ( (ooFF – 32) – 32)

99

1.1. 50 50 ooFF to to ooCC 2. 2. -10 -10 ooFF to to ooCCooC = C = 55 ( (5050 – 32) = 10 – 32) = 10 ooCC ooC = C = 55 ( (- 10 - 10 – 32) = - 23.3 – 32) = - 23.3 ooCC

99 9 9

3. 3. 80 80 ooFF to to ooCC 4. 4. 98.6 98.6 00FF to to ooCCooC = C = 55((8080 – 32) = 26.7 – 32) = 26.7 ooCC ooC = C = 55 ( (98.698.6 – 32) = 37 – 32) = 37 ooCC

99 9 9

B.B. Celsius to Fahrenheit Celsius to Fahrenheit ooF = F = 99 ooCC + 32 + 32 55

1.1. 25 25 ooCC to to ooFF 2.2. 0 0 ooCC to to ooFFooF = F = 99 ( (2525) + 32 = 77 ) + 32 = 77 ooFF ooF = F = 99 ( (00) + 32 = 32 ) + 32 = 32 ooFF

55 5 5

3.3. 100 100 ooCC to to ooFF 4.4. 45 45 ooCC to to ooFF

ooF = F = 99 ( (100100) + 32 = 212 ) + 32 = 212 ooFF ooF = F = 99 ( (4545) + 32 = 113 ) + 32 = 113 ooFF

55 5 5

C.C. Celsius to KelvinCelsius to Kelvin ooK = K = ooCC + 273+ 273oo

1.1. 17 17 ooCC to to ooKK 2.2. 40 40 ooCC to to ooKKooK = K = 1717 + 273 = 290 + 273 = 290 ooKK ooK = K = 4040 + 273 = 313 + 273 = 313 ooKK

3.3. 100 100 ooCC to to ooKK 4.4. 120 120 ooCC to to ooKKooK = K = 100100 + 273 = 373 + 273 = 373 ooKK ooK = K = 120120 + 273 = 393 + 273 = 393 ooKK

D.D. Kelvin to CelsiusKelvin to Celsius ooC = C = ooKK – 273 – 273oo

1.1. 500 500 ooKK to to ooCC 2.2. 0 0 ooK K to to ooCCooC = C = 500500 – 273 = 227 – 273 = 227 ooCC ooC = C = 00 – 273 = - 273 – 273 = - 273 ooCC

3.3. 250 250 ooKK to to ooCC 4.4. 355 355 ooKK to to ooCCooC = C = 250250 – 273 = - 23 – 273 = - 23 ooCC ooC = C = 355355 – 273 = – 273 =

82 82 ooCC

E.E. Fahrenheit to KelvinFahrenheit to Kelvin Step 1:Step 1: ooC = C = 55((ooF – 32)F – 32)

99

Step 2:Step 2: ooK = K = ooC + 273C + 273

1.1. 77 77 ooFF to to ooKK 2.2. 14 14 ooFF to to ooKK

ooC = C = 55((7777 – 32) – 32) ooC = C = 55((1414 – 32) – 32)

99 9 9ooC = 25C = 25 ooC = - 10C = - 10ooK = K = 2525 + 273 + 273 ooK = K = -10-10 + 273 + 273ooK = 298 K = 298 ooKK ooK = 263 K = 263 ooKK

F.F. Kelvin to Fahrenheit Step 1Kelvin to Fahrenheit Step 1 ooC = C = ooK – 273K – 273 Step 2 Step 2 ooF = F = 9 9 ooC + 32C + 32

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1.1. 358 358 ooKK to to ooFF 2.2. 198 198 ooKK to to ooFFooC =C = 358 358 – 273 – 273 ooC = C = 198198 – 273 – 273ooC =C = 85 85 ooCC ooC =C = -75 -75 ooCCooF = F = 99((8585) + 32) + 32 ooF = F = 99((- 75- 75) + 32) + 32

55 5 5

ooF = 153 + 32 F = 153 + 32 ooF = -135 + 32F = -135 + 32 ooF = 185 F = 185 ooFF ooF = - 103 F = - 103 ooFF