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Chapter 1: Problem 33

Make the following conversions: (a) \(72^{\circ} \mathrm{F}\) to \(^{\circ} \mathrm{C},\) (b) \(216.7^{\circ} \mathrm{C}\) to \(^{\circ} \mathrm{F},(\mathbf{c}) 233^{\circ} \mathrm{C}\) to \(\mathrm{K},(\mathbf{d}) 315 \mathrm{K} \mathrm{to}^{\circ} \mathrm{F},(\mathbf{e}) 2500^{\circ} \mathrm{Fto} \mathrm{K},(\mathbf{f}) 0 \mathrm{K}\) to \(^{\circ} \mathrm{F}\)

Short Answer

Expert verified
The short answer for the temperature conversions is as follows: (a) \(22.2^{\circ}\mathrm{C}\) (b) \(422.06^{\circ}\mathrm{F}\) (c) \(506.15 \mathrm{K}\) (d) \(107.33^{\circ}\mathrm{F}\) (e) \(1649.82 \mathrm{K}\) (f) \(-459.67^{\circ}\mathrm{F}\)

Step by step solution

01

Apply the Fahrenheit to Celsius formula

We'll use the Fahrenheit to Celsius formula here: \(°C = \frac{5}{9}(°F - 32)\)
02

Compute the Celsius temperature

Plug in Fahrenheit temperature and solve for Celsius temperature: \(°C = \frac{5}{9}(72°F - 32) = 22.2 °C\) (b) Convert \(216.7^{\circ}\mathrm{C}\) to \(^{\circ}\mathrm{F}\):
03

Apply the Celsius to Fahrenheit formula

We'll use the Celsius to Fahrenheit formula here: \(°F = \frac{9}{5}(°C) +32\)
04

Compute the Fahrenheit temperature

Plug in Celsius temperature and solve for Fahrenheit temperature: \(°F= \frac{9}{5}(216.7°C) + 32 = 422.06 °F\) (c) Convert \(233^{\circ}\mathrm{C}\) to \(K\):
05

Apply the Celsius to Kelvin formula

We'll use the Celsius to Kelvin formula here: \(K = °C + 273.15\)
06

Compute the Kelvin temperature

Plug in Celsius temperature and solve for Kelvin temperature: \(K = 233°C + 273.15 = 506.15 K\) (d) Convert \(315 K\) to \(^{\circ}\mathrm{F}\):
07

Apply Kelvin to Celsius and Celsius to Fahrenheit formulas

First, convert Kelvin to Celsius using \(°C = K - 273.15\), then convert Celsius to Fahrenheit using \(°F = \frac{9}{5}(°C) +32\)
08

Compute Fahrenheit temperature

First, find Celsius temperature,\(°C = 315 K -273.15 = 41.85°C\). Then, find Fahrenheit temperature: \(°F = \frac{9}{5}(41.85°C) + 32 = 107.33 °F\) (e) Convert \(2500^{\circ}\mathrm{F}\) to \(K\):
09

Apply Fahrenheit to Celsius and Celsius to Kelvin formulas

First, convert Fahrenheit to Celsius using \(°C = \frac{5}{9}(°F - 32)\), then convert Celsius to Kelvin using \(K = °C + 273.15\)
10

Compute Kelvin temperature

First, find Celsius temperature, \(°C = \frac{5}{9}(2500°F-32) = 1376.67°C\). Then, find Kelvin temperature: \(K = 1376.67°C + 273.15 = 1649.82 K\) (f) Convert \(0 K\) to \(^{\circ}\mathrm{F}\):
11

Apply Kelvin to Celsius and Celsius to Fahrenheit formulas

First, convert Kelvin to Celsius using \(°C = K - 273.15\), then convert Celsius to Fahrenheit using \(°F = \frac{9}{5}(°C) +32\)
12

Compute Fahrenheit temperature

First, find Celsius temperature, \(°C = 0 K -273.15 = -273.15°C\). Then, find Fahrenheit temperature: \(°F = \frac{9}{5}(-273.15°C) + 32 = -459.67 °F\)

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Most popular questions from this chapter

Classify each of the following as a pure substance or a mixture. If a mixture, indicate whether it is homogeneous or heterogeneous: (a) rice pudding, (b) seawater, (c) magnesium, (d) crushed ice.

Which separation method is better suited for separating a solution of sugar and water into pure substances, filtration or distillation?

What type of quantity (for example, length, volume, density) do the following units indicate? (a) \(\mathrm{mL},(\mathbf{b}) \mathrm{cm}^{2}\) ,\((\mathbf{c}) \mathrm{mm}^{3},(\mathbf{d}) \mathrm{mg} / \mathrm{L},(\mathbf{e}) \mathrm{ps},(\mathbf{f}) \mathrm{nm},(\mathrm{g}) \mathrm{K}\)

Give the derived SI units for each of the following quantities in base Sl units: $$\begin{array}{l}{\text { (a) acceleration }=\text { distance } / \text { time }^{2}} \\ {\text { (b) force }=\text { mass } \times \text { acceleration }} \\ {\text { (c) work }=\text { force } \times \text { distance }} \\ {\text { (d) pressure }=\text { force/area }}\end{array}$$$$ \begin{array}{l}{\text { (e) power }=\text { work/time }} \\ {\text { (f) velocity }=\text { distance } / \text { time }} \\ {\text { (g) energy }=\text { mass } \times \text { (velocity) }^{2}}\end{array} $$

A solid white substance A is heated strongly in the absence of air. It decomposes to form a new white substance \(B\) and a gas C.The gas has exactly the same properties as the product obtained when carbon is burned in an excess of oxygen. Based on these observations, can we determine whether solids \(\mathrm{A}\) and \(\mathrm{B}\) and gas \(\mathrm{C}\) are elements or compounds?
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