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Chapter 1: Problem 26

a) The temperature on a warm summer day is \(87^{\circ} \mathrm{F}\). What is the temperature in \({ }^{\circ} \mathrm{C} ?\) (b) Many scientific data are reported at \(25^{\circ} \mathrm{C}\). What is this temperature in kelvins and in degrees Fahrenheit? (c) Suppose that a recipe calls for an oven temperature of \(400{ }^{\circ} \mathrm{F}\). Convert this temperature to degrees Celsius and to kelvins. (d) Liquid nitrogen boils at \(77 \mathrm{~K}\). Convert this temperature to degrees Fahrenheit and to degrees Celsius.

Short Answer

Expert verified
a) \(30.56^{\circ} \textrm{C}\) b) \(298.15 \textrm{K}\), \(77^{\circ} \textrm{F}\) c) \(204.44^{\circ} \textrm{C}\), \(477.59 \textrm{K}\) d) \(-196.15^{\circ} \textrm{C}\), \(-321.07^{\circ} \textrm{F}\)

Step by step solution

01

Use the Fahrenheit to Celsius formula

Apply the formula: \(C = \dfrac{5}{9}(F - 32)\)
02

Substitute the given temperature

Substitute the given Fahrenheit temperature \(F = 87\) and solve for Celsius temperature: \[C = \dfrac{5}{9}(87 - 32)\]
03

Calculate

Perform the calculation: \[C \approx 30.56^{\circ} \textrm{C}\] The temperature in Celsius is approximately \(30.56^{\circ} \textrm{C}\). b) Convert \(25^{\circ} \textrm{C}\) to Kelvin and Fahrenheit
04

Convert Celsius to Kelvin

Use the formula \(K = C + 273.15\) to convert Celsius to Kelvin: \[K = 25 + 273.15\]
05

Calculate Kelvin temperature

Perform the calculation: \[K \approx 298.15 \textrm{K}\] The temperature in Kelvin is approximately \(298.15 \textrm{K}\).
06

Convert Celsius to Fahrenheit

Use the formula \(F = \dfrac{9}{5}C + 32\) to convert Celsius to Fahrenheit: \[F = \dfrac{9}{5}(25) + 32\]
07

Calculate Fahrenheit temperature

Perform the calculation: \[F \approx 77^{\circ} \textrm{F}\] The temperature in Fahrenheit is approximately \(77^{\circ} \textrm{F}\). c) Convert \(400{ }^{\circ} \textrm{F}\) to Celsius and Kelvin
08

Convert Fahrenheit to Celsius

Apply the formula: \(C = \dfrac{5}{9}(F - 32)\), and substitute the given Fahrenheit temperature \(F = 400\): \[C = \dfrac{5}{9}(400 - 32)\]
09

Calculate Celsius temperature

Perform the calculation: \[C \approx 204.44^{\circ} \textrm{C}\] The temperature in Celsius is approximately \(204.44^{\circ} \textrm{C}\).
10

Convert Celsius to Kelvin

Use the formula \(K = C + 273.15\) to convert Celsius to Kelvin: \[K = 204.44 + 273.15\]
11

Calculate Kelvin temperature

Perform the calculation: \[K \approx 477.59 \textrm{K}\] The temperature in Kelvin is approximately \(477.59 \textrm{K}\). d) Convert \(77 \textrm{K}\) to Fahrenheit and Celsius
12

Convert Kelvin to Celsius

Use the formula \(C = K - 273.15\) to convert Kelvin to Celsius: \[C = 77 - 273.15\]
13

Calculate Celsius temperature

Perform the calculation: \[C \approx -196.15^{\circ} \textrm{C}\] The temperature in Celsius is approximately \(-196.15^{\circ} \textrm{C}\).
14

Convert Celsius to Fahrenheit

Use the formula \(F = \dfrac{9}{5}C + 32\) to convert Celsius to Fahrenheit: \[F = \dfrac{9}{5}(-196.15) + 32\]
15

Calculate Fahrenheit temperature

Perform the calculation: \[F \approx -321.07^{\circ} \textrm{F}\] The temperature in Fahrenheit is approximately \(-321.07^{\circ} \textrm{F}\).

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Most popular questions from this chapter

(a) A bumblebee flies with a ground speed of \(15.2 \mathrm{~m} / \mathrm{s}\). Calculate its speed in \(\mathrm{km} / \mathrm{h}\). (b) The lung capacity of the blue whale is \(5.0 \times 10^{3} \mathrm{~L}\). Convert this volume into gallons. (c) The Statue of Liberty is 151 ft tall. Calculate its height in meters. (d) Bamboo can grow up to \(60.0 \mathrm{~cm} /\) day. Convert this growth rate into inches per hour.

Indicate the number of significant figures in each of the following measured quantities: (a) \(3.774 \mathrm{~km}\) (b) \(205 \mathrm{~m}^{2}\), (c) \(1.700 \mathrm{~cm}\), (d) \(350.00 \mathrm{~K}\), (e) \(307.080 \mathrm{~g}\), (f) \(1.3 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

A \(32.65-\mathrm{g}\) sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is \(50.00 \mathrm{~mL}\). The solid and toluene together weigh \(58.58 \mathrm{~g} .\) The density of toluene at the temperature of the experiment is \(0.864 \mathrm{~g} / \mathrm{mL}\). What is the density of the solid?

What is the number of significant figures in each of the following measured quantities? (a) \(601 \mathrm{~kg}\), (b) \(0.054 \mathrm{~s}\), (c) \(6.3050 \mathrm{~cm}\), (d) \(0.0105 \mathrm{~L}\) (e) \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\) (f) \(400 \mathrm{~g}\).

(a) Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: a gold coin, a cup of coffee, a wood plank. (b) What ambiguities are there in answering part (a) from the descriptions given?
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