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Chapter 15: Problem 18

Express each of the following conversions to four significant digits: a) \(340 \mathrm{Btu} / \mathrm{s}\) to watts b) 3458 degrees to radians c) 25 hectares to square meters d) 240 horsepower to watts e) \(67851.22 \mathrm{kWh}\) to joules f) \(2 \times 10^{-7}\) miles to meters g) \(40 \mathrm{mph}\) to \(\mathrm{km} / \mathrm{s}\)

Short Answer

Expert verified
Question: Convert the following physical quantities from one unit to another and provide your answer with the appropriate significant figures: 1. 340 Btu/s to watts 2. 3458 degrees to radians 3. 25 hectares to square meters 4. 240 horsepower to watts 5. 67851.22 kWh to joules 6. 2 x 10^(-7) miles to meters 7. 40 mph to km/s Answer: 1. \(3.587 \times 10^5 \mathrm{watts}\) 2. \(60.309 \ \mathrm{radians}\) 3. \(2.500 \times 10^5 \mathrm{m^2}\) 4. \(1.790 \times 10^5 \mathrm{watts}\) 5. \(2.442 \times 10^{11} \mathrm{joules}\) 6. \(3.2187 \times 10^{-4} \mathrm{meters}\) 7. \(0.017881 \mathrm{km/s}\)

Step by step solution

01

Convert Btu/s to watts

To convert Btu/s to watts, use the conversion factor: 1 Btu/s = 1,055.06 watts. Therefore, the given value in Btu/s is: $$340 \mathrm{Btu/s} \times \frac{1,055.06 \mathrm{watts}}{1 \mathrm{Btu/s}} = 358,720 \mathrm{watts}$$ Now limit the answer to four significant digits: \(358,720 \mathrm{watts} = 3.587 \times 10^5 \mathrm{watts}\)
02

Convert degrees to radians

To convert degrees to radians, use the conversion factor: \(1^\circ = \frac{\pi}{180} \mathrm{radians}\). So, the given value in degrees is: $$3458^\circ \times \frac{\pi}{180^\circ} = 60.309 \ \mathrm{radians}$$
03

Convert hectares to square meters

To convert hectares to square meters, use the conversion factor: 1 hectare = 10,000 square meters. Then convert the given value: $$25 \mathrm{hectares} \times \frac{10,000 \mathrm{m^2}}{1 \mathrm{hectare}} = 25 \times 10^4 \mathrm{m^2} = 2.500 \times 10^5 \mathrm{m^2}$$
04

Convert horsepower to watts

To convert horsepower to watts, use the conversion factor: 1 horsepower = 745.7 watts. Then convert the given value: $$240 \mathrm{horsepower} \times \frac{745.7 \mathrm{watts}}{1 \mathrm{horsepower}} = 1.790 \times 10^5 \mathrm{watts}$$
05

Convert kWh to joules

To convert kWh to joules, use the conversion factor: \(1 \mathrm{kWh} = 3.6 \times 10^{6} \mathrm{joules}\). Then convert the given value: $$67851.22 \mathrm{kWh} \times \frac{3.6 \times 10^6 \mathrm{joules}}{1 \mathrm{kWh}} = 2.442 \times 10^{11} \mathrm{joules}$$
06

Convert miles to meters

To convert miles to meters, use the conversion factor: \(1 \mathrm{mile} = 1,609.34 \mathrm{meters}\). Then convert the given value: $$2 \times 10^{-7} \mathrm{miles} \times \frac{1,609.34 \mathrm{meters}}{1 \mathrm{mile}} = 3.2187 \times 10^{-4} \mathrm{meters}$$
07

Convert mph to km/s

To convert mph to km/s, first convert mph to m/s using the conversion factor: \(1 \mathrm{mph} = 0.44704 \mathrm{m/s}\). Then convert m/s to km/s by dividing by 1,000. So the given value in mph is: $$40 \mathrm{mph} \times \frac{0.44704 \mathrm{m/s}}{1 \mathrm{mph}} \times \frac{1 \mathrm{km}}{1,000 \mathrm{m}} = 0.017881 \mathrm{km/s}$$

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