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Chapter 1: Problem 76

A Fahrenheit and a Celsius thermometer are immersed in the same medium. At what Celsius temperature will the numerical reading on the Fahrenheit thermometer be (a) \(49^{\circ}\) less than that on the Celsius thermometer; (b) twice that on the Celsius thermometer; (c) one-eighth that on the Celsius thermometer; (d) \(300^{\circ}\) more than that on the Celsius thermometer?

Short Answer

Expert verified
(a) The Celsius temperature at which it will be 49 degrees less on the Fahrenheit thermometer is -59 degrees. (b) The Celsius temperature at which it will be twice on the Fahrenheit thermometer is 160 degrees. (c) The Celsius temperature at which it will be one-eighth on the Fahrenheit thermometer is -176.8 degrees. (d) The Celsius temperature at which it will be 300 degrees more on the Fahrenheit thermometer is 135 degrees.

Step by step solution

01

Understand the Conversion Formula

The first thing to remember is that the conversion from a temperature from Celsius to Fahrenheit is given by the formula: \(F = \frac{9}{5}C + 32\). In this formula, \(F\) represents the temperature in Fahrenheit and \(C\) represents the temperature in Celsius.
02

Formulate and Solve for (a)

(a) From the given condition, we know that the Celsius temperature is given as \(F + 49\). We substitute this into the conversion formula:\[\frac{9}{5}(F + 49) + 32 = F\]Solving this equation, we find \(C = -59\degree\)
03

Formulate and Solve for (b)

(b) For this part, we need the reading on the Fahrenheit scale to be twice that on the Celsius scale. This gives us the equation:\[\frac{9}{5}C + 32 = 2C\]Solving this equation, we find \(C = 160\degree\)
04

Formulate and Solve for (c)

(c) The condition here is that the Celsius temperature is eight times the Fahrenheit temperature. Hence, the equation is:\[\frac{9}{5}C + 32 = \frac{C}{8}\]Solving this equation, we find \(C = -176.8\degree\)
05

Formulate and Solve for (d)

(d) The final condition is that the Fahrenheit temperature is \(300\degree\) more than the Celsius temperature. The equation is:\[\frac{9}{5}C + 32 = C + 300\]Solving this equation, we find \(C = 135\degree\)

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