Question

The atmosphere of Mars is composed almost entirely of carbon dioxide, with an average temperature of -63 degree C. Carbon dioxide is roughly monatomic. a. What is the rms speed of a molecule in Mars atmosphere? b. What speed would a 1 gram paper clip have if it had the same average kinetic energy as a molecule in Mars atmosphere? c. No enhancement this week. Use this extra time to review the first weeks material and bring in questions on Monday.

Answer 1

Given: T= -63°c = 210 k

N= 1

a) The RMS speed of a molecule can be given as:

v_rms= (3kT/m)^1/2

m= mass of one molecule of the gas.

m = 44 gm [ for carbon dioxide gas]

k is the boltzman constant = 1.38×10^-23 J/k

V_rms = [ (3×1.38×10^-23×210)/0.044]^1/2

= 4.45×10^-10 m/s

Average kinetic energy :

KE= (3/2)kT = (3/2)(1.38×10^-23)(210) = 4.34×10^-21 J

b) as kinetic energy is same

KE = 1/2 mv²

v= [2×KE/m]^1/2

= [(2×4.34×10^-21)/(0.001)]^1/2

= 2.95×10^-9 m/s