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Chapter 1: Problem 61

Convert the following Fahrenheit temperatures to the Celsius and Kelvin scales. a. \(-459^{\circ} \mathrm{F}\) , an extremely low temperature b. \(-40 .^{\circ} \mathrm{F}\) , the answer to a trivia question c. \(68^{\circ} \mathrm{F}\) , room temperature d. \(7 \times 10^{7}\) F, temperature required to initiate fusion reactions in the sun

Short Answer

Expert verified
a. -459°F ≈ -273.33°C and 0K b. -40°F = -40°C and 233.15K c. 68°F = 20°C and 293.15K d. \( 7 \times 10^{7} \)°F ≈ \( 3.89 \times 10^{7} \)°C and \( 3.89 \times 10^{7} \)K

Step by step solution

01

Convert Fahrenheit to Celsius

\ Using the formula, we have: \( C = \frac{5}{9} (-459 - 32) = \frac{5}{9} (-491) = -273.33 \)
02

Convert Celsius to Kelvin

\ Now, using the second formula: \( K = -273.33 + 273.15 = 0.18 \approx 0 \) So, -459°F is approximately equal to -273.33°C and 0K. b. Convert -40°F to Celsius and Kelvin:
03

Convert Fahrenheit to Celsius

\ Using the formula, we have: \( C = \frac{5}{9} (-40 - 32) = \frac{5}{9} (-72) = -40 \)
04

Convert Celsius to Kelvin

\ Now, using the second formula: \( K = -40 + 273.15 = 233.15 \) So, -40°F is equal to -40°C and 233.15K. c. Convert 68°F to Celsius and Kelvin:
05

Convert Fahrenheit to Celsius

\ Using the formula, we have: \( C = \frac{5}{9} (68 - 32) = \frac{5}{9} (36) = 20 \)
06

Convert Celsius to Kelvin

\ Now, using the second formula: \( K = 20 + 273.15 = 293.15 \) So, 68°F is equal to 20°C and 293.15K. d. Convert \( 7 \times 10^{7} \)°F to Celsius and Kelvin:
07

Convert Fahrenheit to Celsius

\ Using the formula, we have: \( C = \frac{5}{9} (7 \times 10^{7} - 32) = \frac{5}{9} (7 \times 10^{7} - 32) \approx 3.89 \times 10^{7} \)
08

Convert Celsius to Kelvin

\ Now, using the second formula: \( K = 3.89 \times 10^{7} + 273.15 \approx 3.89 \times 10^{7} \) So, \( 7 \times 10^{7} \)°F is approximately equal to \( 3.89 \times 10^{7} \)°C and \( 3.89 \times 10^{7} \)K.

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Most popular questions from this chapter

Precious metals and gems are measured in troy weights in the English system: $$\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \operatorname{grain} &=0.0648 \mathrm{g} \\ 1 \text { carat } &=0.200 \mathrm{g} \end{aligned}$$ a. The most common English unit of mass is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is 19.3 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

Is the density of a gaseous substance larger or smaller than the density of a liquid or a solid at the same temperature? Why?

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