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Testing a temperature rule of thumb

Testing a temperature rule of thumb

IP 1
7 marks

The exact conversion from a temperature \(C\,^\circ\mathrm{C}\) to \(F\,^\circ\mathrm{F}\) is \(F=1.8C+32\). A rule of thumb gives the estimate \(E=2C+30\).

  1. Find the temperature at which the Celsius and Fahrenheit scales show the same number.[2]
  2. Show that \(E-F=0.2C-2\).[1]
  3. Find the range of Celsius temperatures for which the rule of thumb is within \(2\,^\circ\mathrm{F}\) of the exact value.[3]
  4. Explain why the rule of thumb is poor for an oven at \(200\,^\circ\mathrm{C}\).[1]

Solution:

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Answer:(a) \(-40\,^\circ\mathrm{C}=-40\,^\circ\mathrm{F}\) (b) \(E-F=0.2C-2\) (c) \(0\le C\le20\) (d) the error is \(38\,^\circ\mathrm{F}\) at \(200\,^\circ\mathrm{C}\)

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