# Chapter 13 - Problems - Page 496: 3

(a) When the temperature is $-40^{\circ}C$, which equals $-40^{\circ}F$, the numerical value of Celsius degrees equals the numerical value of Fahrenheit degrees. (b) When the temperature is $575~K$, which equals $575^{\circ}F$, the numerical value of kelvins equals the numerical value of Fahrenheit degrees.

#### Work Step by Step

(a) We can find the temperature when the numerical value of Celsius degrees equals the numerical value of Fahrenheit degrees: $F = \frac{9}{5}C+32$ $F = \frac{9}{5}F+32$ $\frac{4}{5}F = -32$ $F = -40$ When the temperature is $-40^{\circ}C$, which equals $-40^{\circ}F$, the numerical value of Celsius degrees equals the numerical value of Fahrenheit degrees. (b) We can find the temperature when the numerical value of kelvins equals the numerical value of Fahrenheit degrees: $F = \frac{9}{5}C+32$ $F = \frac{9}{5}(K-273.15)+32$ $F = \frac{9}{5}K-459.67$ $F = \frac{9}{5}F-459.67$ $\frac{4}{5}F = 459.67$ $F = 575$ When the temperature is $575~K$, which equals $575^{\circ}F$, the numerical value of kelvins equals the numerical value of Fahrenheit degrees.

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