A centigrade and a Fahrenheit thermometer one dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers \(140^{\circ}\). What is the fall in temperatures as registered by the centigrade thermometer? (A) \(30^{\circ}\) (B) \(40^{\circ}\) (C) \(60^{\circ}\) (D) \(80^{\circ}\)

Short Answer

Expert verified
The fall in temperatures as registered by the centigrade thermometer is \(\boxed{(B) \: 40^{\circ}}\).

Step by step solution

01

Relationship between Fahrenheit and Celsius

The relationship between Fahrenheit (F) and Celsius (C) temperatures can be expressed as: \[F = \frac{9}{5}C + 32\]
02

Determine Initial Boiling Point Temperature

The boiling point of water occurs at a temperature of \(100^{\circ}\) Celsius. We can convert this to Fahrenheit using the formula above: \[F = \frac{9}{5}(100) + 32 = 212^{\circ} \text{ Fahrenheit}\]
03

Calculate Final Temperature in Celsius

The final temperature in Fahrenheit is given as \(140^{\circ}\). To find the corresponding Celsius temperature, we can use the above formula and re-arrange it to solve for C: \[C = \frac{5}{9}(F - 32)\] Then, plug in \(F = 140^{\circ}\): \[C = \frac{5}{9}(140 - 32) = 60^{\circ} \text{ Celsius}\]
04

Find the Fall in Temperatures

Now we know both the initial Celsius temperature (\(100^{\circ}\)) and the final Celsius temperature (\(60^{\circ}\)). Let's find the difference to have the fall in temperature: \[\text{Fall in temperature} = 100^{\circ}C - 60^{\circ}C = 40^{\circ}C\] Therefore, the fall in temperatures as registered by the centigrade thermometer is: \[\boxed{(B) \: 40^{\circ}}\]

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Most popular questions from this chapter

Amount of heat required to raise the temperature of a body through $1 \mathrm{k}$ is called its (A) water equivalent (B) Thermal capacity (C) entropy (D) specific heat

\(100 \mathrm{~g}\) ice at \(0^{\circ} \mathrm{C}\) placed in \(100 \mathrm{~g}\) water at \(100^{\circ} \mathrm{C}\). The final temperature of the mixture will be........ (Latent heat of ice is \(80 \mathrm{Cal} / \mathrm{g}\), and specific heat of water is \(1 \mathrm{Cal} / \mathrm{g} \mathrm{C}^{\circ}\) ) (A) \(10^{\circ} \mathrm{C}\) (B) \(20^{\circ} \mathrm{C}\) (C) \(30^{\circ} \mathrm{C}\) (D) \(50^{\circ} \mathrm{C}\)

The temperature of equal masses of three different liquids \(\mathrm{X}\), \(\mathrm{Y}, \mathrm{Z}\) are \(12^{\circ} \mathrm{C}, 19^{\circ} \mathrm{C}\) and \(28^{\circ} \mathrm{C}\) respectively. The temperature when \(\mathrm{X}\) and \(\mathrm{Y}\) are mixed is \(16^{\circ} \mathrm{C}\) and when \(\mathrm{Y}\) and \(\mathrm{Z}\) are mixed is \(23^{\circ} \mathrm{C}\) what is the temperature when \(\mathrm{X}\) and \(\mathrm{Z}\) are mixed ? (A) \(21.6^{\circ} \mathrm{C}\) (B) \(18.5^{\circ} \mathrm{C}\) (C) \(23.25^{\circ} \mathrm{C}\) (D) \(20.3^{\circ} \mathrm{C}\)

Two liquids of equal volume are thoroughly mixed. If their specific heat are \(c_{1}, c_{2}\), temperatures \(\theta_{1}, \theta_{2}\) and densities \(\mathrm{d}_{1}, \mathrm{~d}_{2}\) respectively. What is the final temperature of the mixture ? (A) $\left\\{\left(\mathrm{d}_{1} \mathrm{c}_{1} \theta_{1}+\mathrm{d}_{2} \mathrm{c}_{2} \theta_{2}\right) /\left(\mathrm{d}_{1} \theta_{1}+\mathrm{d}_{2} \theta_{2}\right)\right\\}$ (B) $\left\\{\left(\mathrm{c}_{1} \theta_{1}+\mathrm{c}_{2} \theta_{2}\right) /\left(\mathrm{d}_{1} \mathrm{c}_{1}+\mathrm{d}_{2} \mathrm{c}_{2}\right)\right\\}$ (C) $\left\\{\left(\mathrm{d}_{1} \theta_{1}+\mathrm{d}_{2} \theta_{2}\right) /\left(\mathrm{c}_{1} \theta_{1}+\mathrm{c}_{2} \theta_{2}\right)\right\\}$ (D) $\left\\{\left(\mathrm{d}_{1} \mathrm{c}_{1} \theta_{1}+\mathrm{d}_{2} \mathrm{c}_{2} \theta_{2}\right) /\left(\mathrm{d}_{1} \mathrm{c}_{1}+\mathrm{d}_{2} \mathrm{c}_{2}\right)\right\\}$

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