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13.1 Temperature  (Page 3/14)

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The relationships between the three common temperature scales is shown in [link] . Temperatures on these scales can be converted using the equations in [link] .

Temperature conversions
To convert from . . . Use this equation . . . Also written as . . .
Celsius to Fahrenheit T º F = 9 5 T º C + 32 size 12{T left (°F right )= { {9} over {5} } T left (°C right )+"32"} {} T º F = 9 5 T º C + 32 size 12{T rSub { size 8{°F} } = { {9} over {5} } T rSub { size 8{°C} } +"32"} {}
Fahrenheit to Celsius T º C = 5 9 T º F − 32 size 12{T left (°C right )= { {5} over {9} } left [T left (°F right ) - "32" right ]} {} T º C = 5 9 T º F − 32 size 12{T rSub { size 8{°C} } = { {5} over {9} } left (T rSub { size 8{°F} } - "32" right )} {}
Celsius to Kelvin T K = T º C + 273 . 15 size 12{T left (K right )=T left (°C right )+"273" "." "15"} {} T K = T º C + 273 . 15 size 12{T rSub { size 8{K} } =T rSub { size 8{°C} } +"273" "." "15"} {}
Kelvin to Celsius T º C = T K − 273 . 15 size 12{T left (°C right )=T left (K right ) - "273" "." "15"} {} T º C = T K − 273 . 15 size 12{T rSub { size 8{°C} } =T rSub { size 8{K} } - "273" "." "15"} {}
Fahrenheit to Kelvin T K = 5 9 T º F − 32 + 273 . 15 size 12{T left (K right )= { {5} over {9} } left [T left (°F right ) - "32" right ]+"273" "." "15"} {} T K = 5 9 T º F − 32 + 273 . 15 size 12{T rSub { size 8{K} } = { {5} over {9} } left (T rSub { size 8{°F} } - "32" right )+"273" "." "15"} {}
Kelvin to Fahrenheit T ( º F ) = 9 5 T K − 273 . 15 + 32 size 12{T \( °F \) = { {9} over {5} } left [T left (K right ) - "273" "." "15" right ]+"32"} {} T º F = 9 5 T K − 273 . 15 + 32 size 12{T rSub { size 8{°F} } = { {9} over {5} } left (T rSub { size 8{K} } - "273" "." "15" right )+"32"} {}

Notice that the conversions between Fahrenheit and Kelvin look quite complicated. In fact, they are simple combinations of the conversions between Fahrenheit and Celsius, and the conversions between Celsius and Kelvin.

Converting between temperature scales: room temperature

“Room temperature” is generally defined to be 25 º C size 12{"25"°C} {} . (a) What is room temperature in º F size 12{°F} {} ? (b) What is it in K?

Strategy

To answer these questions, all we need to do is choose the correct conversion equations and plug in the known values.

Solution for (a)

1. Choose the right equation. To convert from º C size 12{°C} {} to º F size 12{°F} {} , use the equation

T º F = 9 5 T º C + 32 . size 12{T rSub { size 8{°F} } = { {9} over {5} } T rSub { size 8{°C} } +"32" "." } {}

2. Plug the known value into the equation and solve:

T º F = 9 5 25 º C + 32 = 77 º F . size 12{T rSub { size 8{°F} } = { {9} over {5} } "25"°C+"32"="77"°F "." } {}

Solution for (b)

1. Choose the right equation. To convert from º C size 12{°C} {} to K, use the equation

T K = T º C + 273 . 15 . size 12{T rSub { size 8{K} } =T rSub { size 8{°C} } +"273" "." "15" "." } {}

2. Plug the known value into the equation and solve:

T K = 25 º C + 273 . 15 = 298 K . size 12{T rSub { size 8{K} } ="25"°C+"273" "." "15"="298"`K "." } {}
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Converting between temperature scales: the reaumur scale

The Reaumur scale is a temperature scale that was used widely in Europe in the 18th and 19th centuries. On the Reaumur temperature scale, the freezing point of water is 0 º R size 12{0°R} {} and the boiling temperature is 80 º R size 12{"80"°R} {} . If “room temperature” is 25 º C size 12{"25"°C} {} on the Celsius scale, what is it on the Reaumur scale?

Strategy

To answer this question, we must compare the Reaumur scale to the Celsius scale. The difference between the freezing point and boiling point of water on the Reaumur scale is 80 º R size 12{"80"°R} {} . On the Celsius scale it is 100 º C size 12{"100"°C} {} . Therefore 100 º C = 80 º R size 12{"100"°C="80"°R} {} . Both scales start at 0 º size 12{0°} {} for freezing, so we can derive a simple formula to convert between temperatures on the two scales.

Solution

1. Derive a formula to convert from one scale to the other:

T º R = 0 . 8 º R º C × T º C . size 12{T rSub { size 8{°R} } = { {0 "." 8°R} over {°C} } times T rSub { size 8{°C} } "." } {}

2. Plug the known value into the equation and solve:

T º R = 0 . 8 º R º C × 25 º C = 20 º R . size 12{T rSub { size 8{°R} } = { {0 "." 8°R} over {°C} } times "25"°C="20"°R "." } {}
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Temperature ranges in the universe

[link] shows the wide range of temperatures found in the universe. Human beings have been known to survive with body temperatures within a small range, from 24 º C size 12{"24"°C} {} to 44 º C size 12{"44"°C} {} ( 75 º F size 12{ \( "75"°F} {} to 111 º F size 12{"111"°F} {} ). The average normal body temperature is usually given as 37 . 0 º C size 12{"37" "." 0°C} {} ( 98 . 6 º F size 12{"98" "." 6°F} {} ), and variations in this temperature can indicate a medical condition: a fever, an infection, a tumor, or circulatory problems (see [link] ).

This figure consists of four different infrared thermographs of a person's head and neck, taken when the person's head was positioned at four different angles. The person's face and neck are mostly red and orange, with patches of white, green, and yellow. The red and white colors correspond to hot areas. The person's hair ranges in color from green to light blue to dark blue. The blue color corresponds to cold areas.
This image of radiation from a person’s body (an infrared thermograph) shows the location of temperature abnormalities in the upper body. Dark blue corresponds to cold areas and red to white corresponds to hot areas. An elevated temperature might be an indication of malignant tissue (a cancerous tumor in the breast, for example), while a depressed temperature might be due to a decline in blood flow from a clot. In this case, the abnormalities are caused by a condition called hyperhidrosis. (credit: Porcelina81, Wikimedia Commons)
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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