   Chapter 10, Problem 2CQ

Chapter
Section
Textbook Problem

A sealed container contains a fixed volume of a monatomic ideal gas. If the gas temperature is increased by a factor of two, what is the ratio of the final to the initial (a) pressure, (b) average molecular kinetic energy, (c) root-mean-square speed, and (d) internal energy.

(a)

To determine
The ratio of final pressure ( Pf ) and initial pressure ( Pi ).

Explanation

From the Ideal gas equation, the pressure is,

P=nRTV

• n is the number of moles.
• R is the gas constant.
• T is the temperature.
• V is the volume.

At a constant volume, the pressure is directly proportional to the temperature. Therefore, the ratio of final and initial pressure is equal to the ratio of final ( Tf ) and initial temperature ( Ti ).

PfPi=TfTi                                                         (I)

The temperature of the gas is increased by a factor of two

(b)

To determine
The ratio of final average kinetic energy ( KEf ) and initial average kinetic energy ( KEi ).

(c)

To determine
The ratio of final rms speed ( vrmsf ) and initial rms speed ( vrmsi ).

(d)

To determine
The ratio of final internal energy ( Uf ) and initial internal energy ( Ui ).

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