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Chapter 1: Problem 69

At what temperature does the numerical reading on a Celsius thermometer equal that on a Fahrenheit thermometer?

Short Answer

Expert verified
The numerical reading on a Celsius thermometer equals that on a Fahrenheit thermometer at -40 degrees.

Step by step solution

01

Understand the conversion formula between Celsius and Fahrenheit

The conversion formula between Celsius and Fahrenheit is given by \(F = \frac{9}{5}C + 32\), where F represents the temperature in Fahrenheit and C represents the temperature in Celsius. This formula allows one to convert a temperature reading from Celsius to Fahrenheit.
02

Set the values equal to each other

The problem asks for the temperature at which the numerical values on both scales are equal. Therefore, one needs to set C equal to F in the conversion formula, which results in the equation \(C = \frac{9}{5}C + 32\).
03

Solve for C

One can solve this equation for C by first subtracting \(\frac{9}{5}C\) from both sides to get \(-\frac{4}{5}C = 32\). Then, multiplying both sides of the equation by \(-\frac{5}{4}\) gives \(C = -40\). Thus, the Celsius and Fahrenheit scales give the same numeric reading at a temperature of -40 degrees.

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Most popular questions from this chapter

A human brain weighs about \(1 \mathrm{~kg}\) and contains about \(10^{11}\) cells. Assuming that each cell is com pletely filled with water (density \(=1 \mathrm{~g} / \mathrm{mL}\) ), calculate the length of one side of such a cell if it were a cube. If the cells are spread out in a thin layer that is a single cell thick, what is the surface area in square meters?

Write the numbers represented by the following prefixes: (a) mega-, (b) kilo- (c) deci-, (d) centi-, (e) milli-, (f) micro- (g) nano- (h) pico-

A 6.0 -ft person weighs 168 ib. Express this person's height in meters and weight in kilograms. (1 Ib = \(453.6 \mathrm{~g} ; 1 \mathrm{~m}=3.28 \mathrm{ft} .)\)

Does each of the following describe a physical change or a chemical change? (a) The helium gas inside a balloon tends to leak out after a few hours. (b) A flashlight beam slowly gets dimmer and finally goes out. (c) Frozen orange juice is reconstituted by adding water to it. (d) The growth of plants depends on the sun's energy in a process called photosynthesis. (e) A spoonful of table salt dissolves in a bowl of soup.

(a) Normally the human body can endure a temperature of \(105^{\circ} \mathrm{F}\) for only short periods of time without permanent damage to the brain and other vital organs. What is this temperature in degrees Celsius? (b) Ethylene glycol is a liquid organic compound that is used as an antifreeze in car radiators. It freezes at \(-11.5^{\circ} \mathrm{C}\). Calculate its freezing temperature in degrees Fahrenheit. (c) The temperature on the surface of the sun is about \(6300^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit? (d) The ignition temperature of paper is \(451^{\circ} \mathrm{F}\). What is the temperature in degrees Celsius?
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