Physics

Problem

One way of writing the internal energy of a system is

U = \frac{3}{2}NkT

. a. a i State what the terms

N

k

and

T

refer to. ii Show that the internal energy of a system can also be written as

U = \frac{3}{2}nRT

. iii Show also that the internal energy may be written as

U = \frac{3}{2}PV

. b. b Outline four ways in which the internal energy of a system may be changed.

Intuitive explanation

This equation captures the equipartition theorem for an ideal gas: each translational degree of freedom (motion in $x$ , $y$ , $z$ directions) contributes equally to the total energy. The factor $\frac{3}{2}$ comes from having three independent directions, and $kT$ is the characteristic thermal energy per degree of freedom. Understanding this formula means recognizing that internal energy is really just the sum of all the random kinetic energy of particles jiggling around—temperature is just a measure of how vigorously they're moving.

Intuitive explanation

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