Question

Thermodynamics question:

Calculate:

(a) the average translational kinetic energy of a neon atom at room temperature.

(b) the average translational kinetic energy of a golfball at room temperature (in a gas of golfballs).

(c) the root-mean-square speed of a neon atom at room temperature. What is the Mach number for this speed?

(d) the root-mean-square speed of a golfball at room temperature (in a gas of golf- balls).

Answer 1

a)

Since Neon is an example for ideal gas, the average translational kinetic energy is given by,

where k is the Boltzmann constant and T is the temperature.

Then,

b)

Here the case is similar to the previous one. A gas of golf balls is just like an ideal gas. It also possess an average energy (like a monatomic gas like Neon)

c)

The rms speed of a gas is given by,

where R is the universal gas constant, T is the temperature and M is the mass.

Here,

Then,

Mach number is defined by,

where v is the speed of the gas molecules and u is the speed of sound.

Here

Then,

d)

A typical golf ball will have a mass of

Then, the rms speed of the golf ball at room temperature is,