Question

A sealed box contains a monatomic ideal gas. The number of gas atoms per unit volume is 5.00 * 1020 atoms>cm3, and the average translational kinetic energy of each atom is 1.80 * 10-23 J. (a) What is the gas pressure?

Answer 1

To find the gas pressure, multiply the number of gas atoms per unit volume by the average translational kinetic energy.

Step-by-step explanation:

To find the gas pressure, we can use the formula:

Pressure (P) = Number of gas atoms per unit volume (N) × Average translational kinetic energy (KE)

Substituting the given values:

N = 5.00 × 1020 atoms/cm3

KE = 1.80 × 10-23 J

Converting the units:

N = 5.00 × 1020 atoms/cm3 × (1 m/100 cm)3

Now we can calculate the pressure:

P = 5.00 × 1020 atoms/cm3 × 1.80 × 10-23 J

Answer 2

Pressure,P=6×10^3Pa

Step-by-step explanation:

The gas has an ideal gas behaviour and ideal gas equation

PV=NKT

T= V/N p/K ...eq1

Average transitional kinetic energy Ktr=1.8×10-23J

Ktr=3/2KT

T=2/3Ktr/K....eq2

Equating eq1 and 2

V/N p/K = 2/3Ktr/K

Cancelling K on both sides

P= 2/3N/V( Ktr)

Substituting the value of N/V and dividing by 10^-6 to convert cm^3 to m^3

P = 2/3 (5.0×10^20)/10^-6 × 1.8×10^-23

P= 6 ×10^3Pa