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Chapter 8: Problem 1084

A difference of temperature of \(25^{\circ} \mathrm{Cis}\) equivalent to a difference of (A) \(72^{\circ} \mathrm{F}\) (B) \(45^{\circ} \mathrm{F}\) (C) \(32^{\circ} \mathrm{F}\) (D) \(25^{\circ} \mathrm{F}\)

Short Answer

Expert verified
A difference of 25°C is equivalent to a difference of 45°F. To find this, we used the modified temperature conversion formula for differences: \(ΔF = \frac{9}{5}ΔC\), and plugged in the given Celsius difference, resulting in \(ΔF = 25 \times 1.8 = 45\). The correct answer is (B) \(45^{\circ} \mathrm{F}\).

Step by step solution

01

Set up the conversion formula for temperature differences

To find the equivalent difference in Fahrenheit, we should first create a slightly modified version of the Celsius-Fahrenheit conversion formula that excludes the +32 term, which is specific to absolute temperature. The formula, therefore, will be: \(ΔF = \frac{9}{5}ΔC\)
02

Plug in the given Celsius difference

Now, we will plug in the given difference in Celsius (25°C) into our modified conversion formula: \(ΔF = \frac{9}{5}(25)\)
03

Calculate the Fahrenheit difference

Next, multiply 25 by 9/5 (which is 1.8) to get the equivalent difference in Fahrenheit: \(ΔF = 25 \times 1.8\) \(ΔF = 45\)
04

Match the result with the correct multiple-choice option

Our calculated equivalent temperature difference in Fahrenheit is 45°F. Let's find the matching option in the given multiple-choice options: (A) \(72^{\circ} \mathrm{F}\) (B) \(45^{\circ} \mathrm{F}\) (C) \(32^{\circ} \mathrm{F}\) (D) \(25^{\circ} \mathrm{F}\) As we can see, the correct answer is (B) \(45^{\circ} \mathrm{F}\).

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