   Chapter 10, Problem 59GQ

Chapter
Section
Textbook Problem

You have a sample of helium gas at −33 °C, and you want to increase the rms speed of helium atoms by 10.0%. To what temperature should the gas be heated to accomplish this?

Interpretation Introduction

Interpretation: For the given sample of gas under -33oC, the temperature required to increase in the rms speed for the gas by 10% should be determined.

Concept introduction:

The root mean square velocity μ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

Root mean square velocity can be determined,

μrms=(3RTM)1/2 (1)

(gas constant)R=8.314JKmolM=Molarmass

Molar mass: The molar mass of a substance is determined by dividing the given mass of substance by the amount of the substance.

The kinetic energy for the mole of gas is usually directly proportional to temperature.

KETKE=32kTsince,32k = proportionality constant

Explanation

KE=32kT=32(240 K)=360K

The 10% in total value is 36

Therefore, the total kinetic energy is

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