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Chapter 1: Problem 33

Make the following conversions: (a) \(83^{\circ} \mathrm{F}\) to ${ }^{\circ} \mathrm{C}\( (b) \)29^{\circ} \mathrm{C}\( to \){ }^{\circ} \mathrm{F}$ (c) \(294^{\circ} \mathrm{C}\) to \(\mathrm{K}\) (d) \(832 \mathrm{~K}\) to ${ }^{\circ} \mathrm{C}$ (f) \(35^{\circ} \mathrm{F}\) to \(\mathrm{K}\). (e) \(721 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\)

Short Answer

Expert verified
(a) \(83^{\circ} \mathrm{F} \approx 28.33^{\circ} \mathrm{C}\) (b) \(29^{\circ} \mathrm{C} = 84.2^{\circ} \mathrm{F}\) (c) \(294^{\circ} \mathrm{C} = 567.15 \mathrm{~K}\) (d) \(832 \mathrm{~K} = 558.85^{\circ} \mathrm{C}\) (e) \(35^{\circ} \mathrm{F} \approx 274.82 \mathrm{~K}\) (f) \(721 \mathrm{~K} \approx 838.13^{\circ} \mathrm{F}\)

Step by step solution

01

a) 83°F to °C

Use the Fahrenheit to Celsius conversion formula: \(C = \frac{5}{9} (F - 32)\) Let F = 83, then \(C = \frac{5}{9} (83 - 32)\) Calculate the result: \(C = \frac{5}{9} (51) = 28.333\) So, \(83^{\circ} \mathrm{F} \approx 28.33^{\circ} \mathrm{C}\)
02

b) 29°C to °F

Use the Celsius to Fahrenheit conversion formula: \(F = \frac{9}{5} C + 32\) Let C = 29, then \(F = \frac{9}{5} (29) + 32\) Calculate the result: \(F = \frac{9}{5} (29) + 32 = 84.2\) So, \(29^{\circ} \mathrm{C} = 84.2^{\circ} \mathrm{F}\)
03

c) 294°C to K

Use the Celsius to Kelvin conversion formula: \(K = C + 273.15\) Let C = 294, then \(K = 294 + 273.15\) Calculate the result: \(K = 294 + 273.15 = 567.15\) So, \(294^{\circ} \mathrm{C} = 567.15 \mathrm{~K}\)
04

d) 832 K to °C

Use the Kelvin to Celsius conversion formula: \(C = K - 273.15\) Let K = 832, then \(C = 832 - 273.15\) Calculate the result:\(C = 832 - 273.15 = 558.85\) So, \(832 \mathrm{~K} = 558.85^{\circ} \mathrm{C}\)
05

e) 35°F to K

First, convert Fahrenheit to Celsius using the formula: \(C = \frac{5}{9} (F - 32)\) Let F = 35, then \(C = \frac{5}{9} (35 - 32) = 1.666\) Now, convert Celsius to Kelvin using the formula: \(K = C + 273.15\) Let C = 1.666, then \(K = 1.666 + 273.15 = 274.816\) So, \(35^{\circ} \mathrm{F} \approx 274.82 \mathrm{~K}\)
06

f) 721 K to °F

First, convert Kelvin to Celsius using the formula: \(C = K - 273.15\) Let K = 721, then \(C = 721 - 273.15 = 447.85\) Now, convert Celsius to Fahrenheit using the formula: \(F = \frac{9}{5} C + 32\) Let C = 447.85, then \(F = \frac{9}{5} (447.85) + 32 = 838.13\) So, \(721 \mathrm{~K} \approx 838.13^{\circ} \mathrm{F}\)

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