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Chapter 2: Problem 139

Solve each equation for the underlined quantity: (a) \({ }^{\circ} \mathrm{F}=9 / 5^{\circ} \mathrm{C}+32\) (b) \(P V=n R T\) (c) \(E=h c / \underline{\lambda}\)

Short Answer

Expert verified
\( ^\circ C= \frac{5}{9}({ ^\circ F}-32) \), \( P= \frac{nRT}{V} \), and \( \lambda= \frac{hc}{E} \).

Step by step solution

01

Identify the parts of the equations

This step is essential to understand each equation and what each symbol represents. (a) The given equation is the temperature conversion formula between degrees Fahrenheit (°F) and degrees Celsius (°C). (b) The given equation is the ideal gas equation, where P represents pressure, V represents volume, n represents the amount of gas in moles, R is the ideal gas constant, and T is the temperature. (c) The given equation represents the energy of a photon. The energy is E, h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. Now that we understand each equation, we can begin solving them.
02

Solve the equation (a) for °C

To solve the equation for °C, follow these steps: 1. Subtract 32 from both sides of the equation. 2. Multiply both sides of the equation by 5/9. \( ^\circ C= \frac{5}{9}({ ^\circ F}-32) \)
03

Solve the equation (b) for P

To solve the equation for P, follow these steps: 1. Divide both sides of the equation by V. \( P= \frac{nRT}{V} \)
04

Solve the equation (c) for λ

To solve the equation for λ, follow these steps: 1. Multiply both sides of the equation by λ. 2. Divide both sides of the equation by E. \( \lambda= \frac{hc}{E} \) The solutions for each equation are: (a) \( ^\circ C= \frac{5}{9}({ ^\circ F}-32) \) (b) \( P= \frac{nRT}{V} \) (c) \( \lambda= \frac{hc}{E} \)

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Most popular questions from this chapter

Without doing any numerical calculations, determine which would have the smallest volume: (a) \(50 \mathrm{~g}\) of water (density \(=1.0 \mathrm{~g} / \mathrm{mL}\) ) (b) \(50 \mathrm{~g}\) of salt water (density \(=2.3 \mathrm{~g} / \mathrm{mL}\) ) (c) \(50 \mathrm{~g}\) of mercury (density \(=13.6 \mathrm{~g} / \mathrm{mL}\) ) (d) \(50 \mathrm{~g}\) of alcohol (density \(=0.89 \mathrm{~g} / \mathrm{mL}\) ) Explain your reasoning.

Round each number to three significant digits and express the answer in scientific notation: (a) \(0.592861\) (b) 438932 (c) \(0.000073978\) (d) \(0.235469\) (e) \(82.550\) (f) \(529.8\)

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