Explanation Given data: A scientist measures the speed of sound in a monatomic gas. The speed of sound measured by the scientist in a monatomic gas ( v sound ) is 449 m s . The temperature at which the scientist measured the speed of the sound ( T ° C ) is 20 ° C . Formula used: Refer to the equation (15.3) in the textbook, and write the expression for speed of the sound in the gases as follows. v sound = γ R T M (1) Here, γ is the constant, which is 1.67 for the monatomic gases, R is the gas constant, which is 8.31 J mol ⋅ K , T is the temperature (in Kelvin) at which the speed of the sound is measured, and M is the molar mass of the monatomic gas. Explanation: Write the expression for conversion factor to convert the given temperature in terms of Kelvin as follows. T = ( T ° C + 273 ) K Substitute 20 for T ° C , T = ( 20 + 273 ) K =293 K Finding the element that exists in the monatomic gas: Rearrange the expression in equation (1) for the molar mass of the monatomic gas as follows. ( v sound ) 2 = γ R T M M = γ R T ( v sound ) 2 Substitute 1.67 for γ , 8.31 J mol ⋅ K for R , 293 K for T , and 449 m s for v sound , M = ( 1

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

4th Edition

ISBN: 9780134700502

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Chapter 15, Problem 5P

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To find: The element exists in the monatomic gas in which the scientist measures the speed of the sound as 449 ms.

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Chapter 15, Problem 4P

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Chapter 15 Solutions

College Physics: A Strategic Approach, Books a la Carte Edition (4th Edition)

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The element exists in the monatomic gas in which the scientist measures the speed of the sound as 449 m s .

To find: The element exists in the monatomic gas in which the scientist measures the speed of the sound as 449 ms.

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Chapter 15 Solutions