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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

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 \(40.0^{\circ} \mathrm{C}\).

Which object has the higher temperature after being left outside for an entire winter night: a metal door knob or a rug? a) The metal door knob has the higher temperature. b) The rug has the higher temperature. c) Both have the same temperature. d) It depends on the outside temperature.

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?

You are building a device for monitoring ultracold environments. Because the device will be used in environments where its temperature will change by \(200 .{ }^{\circ} \mathrm{C}\) in \(3.00 \mathrm{~s}\), it must have the ability to withstand thermal shock (rapid temperature changes). The volume of the device is \(5.00 \cdot 10^{-5} \mathrm{~m}^{3}\), and if the volume changes by \(1.00 \cdot 10^{-7} \mathrm{~m}^{3}\) in a time interval of \(5.00 \mathrm{~s}\), the device will crack and be rendered useless. What is the maximum volume expansion coefficient that the material you use to build the device can have?

The lowest air temperature recorded on Earth is \(-129^{\circ} \mathrm{F}\) in Antarctica. Convert this temperature to the Celsius scale.
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