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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U  =  3 2 P V .

To determine
The internal energy of a monatomic ideal gas.

Explanation

Given Info:

Pressure of the monatomic ideal gas is P.

Volume occupied by monatomic ideal gas is V.

Kinetic theory of gas explains the properties of the gas in terms of the motion and interaction of microscopic particles of the gas.

From kinetic theory, the average kinetic energy per molecule is,

KE¯mol=32kBT       (1)

    • kB is the Boltzmann man constant
    • T is the temperature

Substitute RNA for kB in equation (1) to find the average kinetic energy of the molecules,

KE¯molecule=32(RNA)T x

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