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Chapter 17: Problem 7

At what temperature do the Celsius and Fahrenheit temperature scales have the same numeric value? a) -40 degrees b) 0 degrees c) 40 degrees d) 100 degrees

Short Answer

Expert verified
a) -40 degrees b) 0 degrees c) 40 degrees d) 100 degrees Answer: a) -40 degrees

Step by step solution

01

Set up the equation

Since we're looking for when the Celsius and Fahrenheit scales have the same numeric value, we can represent that as: C = F Now, let's use the Fahrenheit to Celsius conversion formula and replace F with C: C = (9/5) * C + 32
02

Solve for C

To solve for C, we need to get C by itself on one side of the equation: C - (9/5) * C = 32 First, let's get a common denominator to combine the C terms. This means multiplying the first term (C) by 5/5: (5/5) * C - (9/5) * C = 32 This simplifies to: (5 - 9) / 5 * C = 32 Now we have: -4/5 * C = 32 To get C by itself, we will multiply both sides of the equation by -5/4: C = 32 * (-5/4) This simplifies to: C = -40 So the Celsius temperature at which the Celsius and Fahrenheit temperature scales have the same numeric value is -40 degrees, which corresponds to option (a).

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Most popular questions from this chapter

When a 50.0 -m-long metal pipe is heated from \(10.0^{\circ} \mathrm{C}\) to \(40.0^{\circ} \mathrm{C}\), it lengthens by \(2.85 \mathrm{~cm}\). a) Determine the linear expansion coefficient. b) What type of metal is the pipe made of?

The Rankine temperature scale is an absolute temperature scale that uses Fahrenheit degrees; that is, temperatures are measured in Fahrenheit degrees, starting at absolute zero. Find the relationships between temperature values on the Rankine scale and those on the Fahrenheit, Kelvin, and Celsius scales.

A solid cylinder and a cylindrical shell, of identical radius and length and made of the same material, experience the same temperature increase \(\Delta T .\) Which of the two will expand to a larger outer radius?

A piece of dry ice (solid carbon dioxide) sitting in a classroom has a temperature of approximately \(-79^{\circ} \mathrm{C}\) a) What is this temperature in kelvins? b) What is this temperature in degrees Fahrenheit?

A medical device used for handling tissue samples has two metal screws, one \(20.0 \mathrm{~cm}\) long and made from brass \(\left(\alpha_{\mathrm{b}}=18.9 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)\) and the other \(30.0 \mathrm{~cm}\) long and made from aluminum \(\left(\alpha_{\mathrm{a}}=23.0 \cdot 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\right)\). A gap of \(1.00 \mathrm{~mm}\) exists between the ends of the screws at \(22.0^{\circ} \mathrm{C}\). At what temperature will the two screws touch?
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