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Chapter 19: Q21P (page 578)

Question: The lowest possible temperature in outer space is 2.7 K. What is the rms speed of hydrogen molecules at this temperature? (The molar mass is2.02脳10-3kg/mol).

Short Answer

Expert verified

Answer:

The RMS speed of the hydrogen molecules is 1.8脳102m/s.

Step by step solution

01

Given data

The temperature is T = 2.7 K

The molar mass of hydrogen molecules is,M=2.02脳10-3kg/mol

02

Concept introduction

We can find the rms speed using its formula in terms of R, temperature, and molar mass.

The expression for the RMS speed is given by,

v=3RTM

03

Calculate the rms speed of hydrogen molecules at the given temperature 

The RMS speed of hydrogen molecules is

v=3RTM

Molar mass of hydrogen isM=2.02脳10-3kg/mol

v=38.3142.72.02脳10-3v=182.58鈮�1.8脳102m/s

Therefore the RMS speed of the hydrogen molecules is1.8脳102m/s .

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Most popular questions from this chapter

  1. An ideal gas initially at pressurep0 undergoes free expansion until its volume is 3.00times its initial volume. What then is the ratio of its pressure to p0?
  2. The gas is next slowly and adiabatically compressed back to its original volume. The pressure after compression is(3.00)1/3p0 . Is the gas monoatomic, diatomic or polyatomic?
  3. What is the ratio of the average kinetic energy per molecule in this final state to that in initial state?

Ten particles are moving with the following speeds: four at200鈥�m/s, two at500鈥�m/s, and four at600鈥�m/s. Calculate their

a) Average speed

b) Rms speed

c) Isvrms>vavg?

The atmospheric density at an altitude of2500鈥�km is about 1molecule/cm3.

  1. Assuming the molecular diameter of 2.0脳10-8cm , find the mean free path predicted by equation 位=12鈥�蟺d2N/V
  2. Explain whether the predicted value is meaningful.

Question: From the knowledge that Cv , the molar specific heat at constant volume, for a gas in a container is 5.0 R , calculate the ratio of the speed of sound in that gas to the rms speed of the molecules, for gas temperature T. (Hint: See Problem 91.)

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