Temperature Conversion and Algebraic Expressions
Learn about converting temperatures between Fahrenheit, Celsius, and Kelvin, understand algebraic expressions for temperature conversion, and find temperatures where Fahrenheit and Celsius numbers match. Discover the relationships between different temperature scales and how to express them in equations and graphs.
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Presentation Transcript
Temperature Yan 02/26/2020
What is the temperature (T) outside? Do you think 40 degree is too hot or too cold? A simple number is meaningless. One need to include the unit. Fahrenheit F used by US, and a few other places. Celsius C used by 200+ countries. Kelvin K used by scientists. Learn to convert between them. F -> C Communicate with people from other countries. F -> K and C -> K A scientifically better way to express the temperature.
What are the temperatures (T) in F and C Room temperature. 75.2 F 24 C Normal body temperature. 98.6 F 37.0 C Freezing temperature. 32 F 0 C Boiling temperature. 212 F 100 C
Plot the temperature on a Figure Room temperature. 75.2 F 24 C Normal body temperature. 98.6 F 37.0 C Freezing temperature. 32 F 0 C Boiling temperature. 212 F 100 C 200 200 160 160 temperature in F temperature in F 120 120 80 80 40 40 0 0 -40 -40 0 0 100 100 50 50 temperature in C temperature in C
Convert to algebraic expression y 212 Note the temp. in F as y Note the temp. in C as x y = m*x+b 200 160 temperature in F 120 What is b (y_intercept)? b=32 212-32=180 80 What is m (slope)? m=180/100=1.8 40 32 100-0=100 0 x y = 1.8 * x + 32 -40 0 100 50 temperature in C [temp. in F] = 1.8 * [temp. in C] + 32
Double check [temp. in F] = 1.8 * [temp. in C] + 32 Room temperature: 75.2 F 24 C y = 1.8 * x + 32 = 1.8 * 24+32 = 43.2+32 = 75.2 y = 1.8 * x + 32 What is -273.15 C in F? Agrees! Could you find a temperature where the number in Fahrenheit and Celsius equals to each other?
Could you find a temperature where the number in Fahrenheit and Celsius equals to each other? [temp. in F] = 1.8 * [temp. in C] + 32 Think in equations: [the temp. in F ] = [the temp. in C ] y = x y = 1.8 * x + 32 200 200 Two ways to solve: Draw the line on the graph. Solve algebraically. 160 160 temperature in F temperature in F 120 120 80 80 40 40 x = 1.8 * x + 32 0 0 -40 -40 0 0 100 100 50 50 temperature in C temperature in C
Convert back from F to C [temp. in F] = 1.8 * [temp. in C] + 32 y = 1.8 * x + 32 Obtain an expression for x. How? y = 1.8 * x + 32 y 32 = 1.8 * x (y 32)/1.8 = x x= (y 32)/1.8 [temp. in C] = ([temp. in F] - 32)/1.8
Transformation to the thermometer Algebra is boring? Let s do it using graph.
Transformation to the thermometer Shift left by -32 (y 32)
Transformation to the thermometer Shift left by -32 (y 32) Shrink to 1.8 smaller x= (y 32)/1.8
Transformation to the thermometer Shift left by -32 (y 32) (zoom in to see details) Shrink to 1.8 smaller x= (y 32)/1.8
Transformation to the thermometer shift right by 17.78 (x+17.78)
Transformation to the thermometer shift right by 17.78 Expand by a a factor of 1.8 y= (x+17.78)*1.8 = 1.8*x +32 (x+17.78)
