Temperature Physics Example 2

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Example 2

medium
At what temperature do the Celsius and Fahrenheit scales read the same value?

Solution

  1. 1
    Set TC=TF=TT_C = T_F = T and use the conversion formula: T=95T+32T = \frac{9}{5}T + 32.
  2. 2
    T−95T=32  ⟹  −45T=32  ⟹  T=−40T - \frac{9}{5}T = 32 \implies -\frac{4}{5}T = 32 \implies T = -40
  3. 3
    At −40°-40°, both scales give the same reading: −40°C=−40°F-40°\text{C} = -40°\text{F}.

Answer

T=−40° (both C and F)T = -40° \text{ (both C and F)}
The Celsius and Fahrenheit scales intersect at exactly −40°-40°. This is a unique mathematical result of the linear relationship between the two temperature scales.

About Temperature

A measure of the average kinetic energy of the particles in a substance, determining how hot or cold it is.

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More Temperature Examples

Example 1 easy

Convert [formula] (human body temperature) to Fahrenheit and Kelvin.

Example 3 medium

Liquid nitrogen boils at [formula]. What is this temperature in Celsius and Fahrenheit?

Example 4 hard

Two objects are at [formula] and [formula]. One student says the hotter object is 'twice as hot.' Is

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