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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

For a class demonstration, your physics instructor uniformly heats a bimetallic strip that is held in a horizontal orientation. As a result, the bimetallic strip bends upward. This tells you that the coefficient of linear thermal expansion for metal T, on the top is _____ that of metal B, on the bottom. a) smaller than b) larger than c) equal to

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\(\cdot 17.41\) A clock based on a simple pendulum is situated outdoors in Anchorage, Alaska. The pendulum consists of a mass of 1.00 kg that is hanging from a thin brass rod that is \(2.000 \mathrm{~m}\) long. The clock is calibrated perfectly during a summer day with an average temperature of \(25.0^{\circ} \mathrm{C}\). During the winter, when the average temperature over one 24 -h period is \(-20.0^{\circ} \mathrm{C}\), find the time elapsed for that period according to the simple pendulum clock.

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A steel rod of length \(1.0000 \mathrm{~m}\) and cross-sectional area \(5.00 \cdot 10^{-4} \mathrm{~m}^{2}\) is placed snugly against two immobile end points. The rod is initially placed when the temperature is \(0^{\circ} \mathrm{C}\). Find the stress in the rod when the temperature rises to \(40.0^{\circ} \mathrm{C}\).
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