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Chapter 1: Problem 52

A thermometer gives a reading of \(24.2^{\circ} \mathrm{C} \pm 0.1^{\circ} \mathrm{C}\). Calculate the temperature in degrees Fahrenheit. What is the uncertainty?

Short Answer

Expert verified
Given the temperature reading of \(24.2C \pm 0.1C\), after doing the conversion and calculation of uncertainty, obtain the temperature in Fahrenheit with its associated uncertainty.

Step by step solution

01

Conversion of Temperature to Fahrenheit

The conversion formula for Celsius (C) to Fahrenheit (F) is given by \( F = 9/5C + 32 \). Substituting the given temperature reading of \(24.2^{\circ} C\), the temperature in Fahrenheit is calculated as: \( F = 9/5(24.2) + 32 \).
02

Compute the Temperature

Calculate the result from Step 1 to find the temperature in Fahrenheit.
03

Calculate the Uncertainty in Fahrenheit

The uncertainty in the Fahrenheit scale is \( ΔF = 9/5 ΔC \) by differentiating the conversion formula. Thus, calculate the new uncertainty \( ΔF = 9/5 * 0.1 \) using the given uncertainty in Celsius.
04

Compute Uncertainty in Fahrenheit

Calculate the result from Step 3 to find the uncertainty in Fahrenheit.

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Most popular questions from this chapter

The medicinal thermometer commonly used in homes can be read to \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor's office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

A student is given a crucible and asked to prove whether it is made of pure platinum. She first weighs the crucible in air and then weighs it suspended in water (density \(\left.=0.9986 \mathrm{~g} / \mathrm{cm}^{3}\right)\). The readings are \(860.2 \mathrm{~g}\) and \(820.2 \mathrm{~g}\), respectively. Given that the density of platinum is \(21.45 \mathrm{~g} / \mathrm{cm}^{3},\) what should her conclusion be based on these measurements? (Hint: An object suspended in a fluid is buoyed up by the mass of the fluid displaced by the object. Neglect the buoyancy of air.)

A bank teller is asked to assemble "one-dollar" sets of coins for his clients. Each set is made of three quarters, one nickel, and two dimes. The masses of the coins are: quarter: \(5.645 \mathrm{~g}\); nickel: \(4.967 \mathrm{~g}\); dime: \(2.316 \mathrm{~g}\). What is the maximum number of sets that can be assembled from \(33.871 \mathrm{~kg}\) of quarters, \(10.432 \mathrm{~kg}\) of nickels, and \(7.990 \mathrm{~kg}\) of dimes? What is the total mass (in g) of this collection of coins?

Express the answers to these in scientific notation: (a) \(145.75+\left(2.3 \times 10^{-1}\right)\) (b) \(79,500 \div\left(2.5 \times 10^{2}\right)\) (c) \(\left(7.0 \times 10^{-3}\right)-\left(8.0 \times 10^{-4}\right)\) (d) \(\left(1.0 \times 10^{4}\right) \times\left(9.9 \times 10^{6}\right)\)

What is the number of significant figures in each of these measured quantities? (a) 4867 miles, (b) \(56 \mathrm{~mL}\) (c) 60,104 tons, (d) \(2900 \mathrm{~g}\).
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