Fiveable

๐Ÿ’ฏMath for Non-Math Majors Unit 9 Review

QR code for Math for Non-Math Majors practice questions

9.5 Measuring Temperature

๐Ÿ’ฏMath for Non-Math Majors
Unit 9 Review

9.5 Measuring Temperature

Written by the Fiveable Content Team โ€ข Last updated September 2025
Written by the Fiveable Content Team โ€ข Last updated September 2025
๐Ÿ’ฏMath for Non-Math Majors
Unit & Topic Study Guides

Temperature is all about molecular motion. As things heat up, molecules move faster and spread out. When they cool down, molecules slow down and get closer together. This affects how substances behave and is key to understanding many everyday phenomena.

Measuring temperature involves different scales like Fahrenheit and Celsius. Converting between them is useful for cooking, weather forecasts, and science. Understanding temperature helps us make sense of the world around us, from why bridges expand to how our bodies regulate heat.

Temperature and Molecular Motion

Temperature and molecular motion

  • Measures the average kinetic energy of molecules in a substance
    • Energy of motion possessed by molecules
  • Increases cause molecules to move faster and collide more frequently
    • Leads to expansion as molecules spread out due to increased motion (gases, liquids)
  • Decreases cause molecules to move slower and collide less frequently
    • Leads to contraction as molecules move closer together due to decreased motion (solids)
  • Measured using a thermometer

Fahrenheit vs Celsius conversions

  • Two common temperature scales used to measure temperature
  • Fahrenheit to Celsius conversion: $ยฐC = (ยฐF - 32) \times \frac{5}{9}$
    1. Subtract 32 from the Fahrenheit temperature
    2. Multiply the result by $\frac{5}{9}$
  • Celsius to Fahrenheit conversion: $ยฐF = (ยฐC \times \frac{9}{5}) + 32$
    1. Multiply the Celsius temperature by $\frac{9}{5}$
    2. Add 32 to the result
  • Mental math approximations for quick estimates
    • Celsius from Fahrenheit: subtract 30 from ยฐF and divide by 2 (86ยฐF โ‰ˆ 28ยฐC)
    • Fahrenheit from Celsius: double ยฐC and add 30 (25ยฐC โ‰ˆ 80ยฐF)

Temperature Scales and Concepts

  • Kelvin: An absolute temperature scale with 0 K representing absolute zero
  • Absolute zero: The lowest possible temperature where molecular motion theoretically stops
  • Thermal expansion: The tendency of matter to change in volume in response to temperature changes
  • Heat transfer: The movement of thermal energy from one object or system to another

Temperature in real-world applications

  • Cooking and baking require temperature conversions
    • Recipe calls for 180ยฐC, convert to Fahrenheit: $ยฐF = (180 \times \frac{9}{5}) + 32 = 356ยฐF$
  • Weather forecasts and climate data use different scales
    • London temperature 20ยฐC, convert to Fahrenheit: $ยฐF = (20 \times \frac{9}{5}) + 32 = 68ยฐF$
  • Temperature changes affect properties and behavior of substances
    • Water freezes at 0ยฐC (32ยฐF) and boils at 100ยฐC (212ยฐF) at standard atmospheric pressure
    • Bridges and railways expand and contract due to temperature changes
      • Expansion joints and gaps prevent damage (Golden Gate Bridge, San Francisco)