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Chapter 19: Q20P (page 578)

Question: Calculate the RMS speed of helium atoms at 1000k. Molar mass of helium atoms is4.0026gmol.

Short Answer

Expert verified

Answer

The RMS speed of helium atoms at 1000 k is2.50脳103ms.

Step by step solution

01

Given

The temperature is T = 1000 k

02

Determining the concept

Find the RMS speed from its formula in terms of R, temperature, and molar mass.

Formula is as follow:

v=3RTM

Here, M is mass, Tis temperature, v is velocity and R is universal gas constant.

03

Determining the RMS speed of helium atoms at 1000 K

The RMS speed of helium atoms is,

v=3RTM

Molar mass of helium is,

M=4脳10-3kgmol

Substitute the values in the equation for velocity and solve as:

v=38.31410004脳10-3v=2497鈮�2.50脳103ms

Hence, the RMS speed of helium atoms at 1000 K is 2.50脳103ms.

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Most popular questions from this chapter

Question: Supposeof an ideal gas undergoes an isothermal expansion as energy is added to it as heat Q. If figure shows the final volume Vf versus Q, what is the gas temperature? The scale of the vertical axis is set by Vfs=.30m3, and the scale of the horizontal axis is set by Qs=1200J

Under constant pressure, the temperature of2.00鈥�molof an ideal monoatomic gas is raised15.0鈥�K. What are

  1. The workW done by the gas
  2. The energy transferred as heatQ
  3. The change螖Eintin the internal energy of the gas
  4. The change螖Kin the average kinetic energy per atom?

Question: Figureshows a cycle consisting of five paths: AB is isothermal at 300K, BC is adiabatic with work=5.0J, CD is at a constant pressure of, DE is isothermal, and EA is adiabatic with a change in internal energy of 8.0J. What is the change in internal energy of the gas along path CD?
  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?

A hydrogen molecule (diameter 1.0脳10-8cm), travelling at the rms speed, escapes from a 4000鈥�K furnace into a chamber containing coldargon atoms (diameter) at a density of.

a) What is the speed of the hydrogen molecule?

b) If it collides with an argon atom, what is the closest their centres can be, considering each as spherical?

c) What is the initial number of collisions per second experienced by the hydrogen molecule? (Hint: Assume that the argon atoms are stationary. Then the mean free path of the hydrogen molecule is given by

Mean free path=1蟺d2鈥�N/V
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