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?

Question

Physics

Brett Rivera

12 May, 20:45

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?

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Answers (1)

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Kaitlynn Farrell · Answer 1

Pressure, P=6*10^3Pa

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