PHYS-2210 Study Guide - Final Guide: Root Mean Square, Ideal Gas, Ideal Gas Law

65 views10 pages

burgundywildebeest589

2 Apr 2016

School

Department

Course

Professor

For unlimited access to Study Guides, a Grade+ subscription is required.

Document Summary

Kinetic theory attempts to model the random collisions of gas molecules on the walls of their container and relate it to the pressure (a macroscopic variable) they produce. What follows is a simplified version of kinetic theory used to relate pressure to the velocities of molecules in an ideal gas. Imagine a cube of length of side d full of ideal gas. The gas molecules are not stationary by have a random distribution of velocities. Some molecules move fast and others move slowly, and the directions of these velocities are also random. First we consider what happens to one molecule and then consider the combined effect of all n molecules. Image one of these molecules of mass m striking the wall of its container: Notice only the x-component of the velocity contributes to the force on the wall because the y and z components are parallel to the surface and don"t push on the wall.

Related Questions

1. The ideal gas law is given as PV = nRT, where n is the number ofmoles of gas (1 mole = 6.02 * 10^23 molecules) and R is theuniversal gas constant (R = 8.31 J/mol-k). Explain why the productof pressure and volume is constant in an isothermal process.Explain why the ratio of pressure and temperature is constant in anisovolumetric process.

2. Explain the origin of pressure of gas in a container based onthe motions of molecules in the gas, their average momentum, andtheir collisions with the walls of the container.

3. Based on the kinetic theory definition of temperature as theaverage kinetic energy of a molecule in an ideal gas and youranswer to question 1, explain why the pressure of a gas increaseswhen it is compressed while kept at a constant temperature.

4. Based on the kinetic theory definition of temperature as theaverage kinetic energy of a molecule in an ideal gas and youranswer to question 1, explain why the pressure of a gas increaseswhen its temperature is increased while its volume is keptconstant.

The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: The gas is composed of pointlike particles separated by comparatively large distances. The gas molecules are in continual random motion with collisions being perfectly elastic. The gas molecules exert no long-range forces on each other. One of the most important microscopic properties of gas molecules is velocity. There are several different ways to describe statistically the average velocity of a molecule in a gas. The most obvious measure is the average velocity Vavg. However, since the molecules in a gas are moving in random directions, the average velocity is approximately zero. Another measure of velocity is (V^2)avg, the average squared velocity. Since the square of velocity is always positive, this measure does not average to zero over the entire gas. A third measure is the root-mean-square (rms) speed,Vrms , equal to the square root of (V^2)avg. The rms speed is a good approximation of the the typical speed of the molecules in a gas. This histogram (Figure 1) shows a theoretical distribution of speeds of molecules in a sample of nitrogen () gas. In this problem, you'll use the histogram to compute properties of the gas.

Part A

What is the average speed

of the molecules in the gas?

Part B

Because the kinetic energy of a single molecule is related to its velocity squared, the best measure of the kinetic energy of the entire gas is obtained by computing the mean squared velocity, $(v^2)_{\rm avg}$ , or its square root. The quantityis more common than $(v^2)_{\rm avg}$ because it has the dimensions of velocity instead of the less-familiar velocity-squared.

What is the rms speedof the molecules in the nitrogen gas?

Express your answer numerically to three significant digits.

Part C

What is the temperatureof the sample of $\rm N_2$ gas described in the histogram?

Express your answer in degrees Celsius to three significant figues.

viridianjackal166

A magnetic field of 0.1T forces a proton beam of 1.5 mA to move ina circle of radius 0.1 m. The plane of the circle is perpendicularto the magnetic field.

47. Of the following, which is the best estimate of the speed of aproton in the beam as it moves in the circle?
(A) 10-2 m/s (B) 103 m/s (C) 106 m/s (D) 108 m/s (E) 1015 m/s

52. An ideal gas is initially in a state that corresponds to point1 on the graph above, where it has presÂ¬sure p1, volume V1, andtemperature T1. The gas undergoes an isothermal process representedby the curve shown, which takes it to a final state 3 attemperature T3. If T2 and T4 are the temperaÂ¬tures the gas wouldhave at points 2 and 4, respecÂ¬tively, which of the followingrelationships is true?
(A) T1 < T3 (B) T1 < T2 (C) T1 < T4 (D) T1 = T2 (E) T1 =T4

53. The absolute temperature of a sample of monatomic ideal gas isdoubled at constant volume. What effect, if any, does this have onthe pressure and density of the sample of gas?
Pressure Density
(A) Remains the same Remains the same
(B) Remains the same Doubles
(C) Doubles Remains the same
(D) Doubles Is multiplied by a factor of 4
(E) Is multiplied by a factor of 4 Doubles

62. A sample of an ideal gas is in a tank of constant volume. Thesample absorbs heat energy so that its temperature changes from 300K to 600 K. If v1 is the average speed of the gas molecules beforethe absorption of heat and v2 is their average speed after theabsorption of heat, what is the ratio v2/ v1 ?
(A) 1/2 (B) 1 (C) (D) 2 (E) 4

63. Two people of unequal mass are initially standing still on icewith negligible friction. They then simulÂ¬taneously push each otherhorizontally. Afterward, which of the following is true?
(A) The kinetic energies of the two people are equal.
(B) The speeds of the two people are equal.
(C) The momenta of the two people are of equal magnitude.
(D) The center of mass of the two person system moves in thedirection of the less massive person.
(E) The less massive person has a smaller initial acceleration thanthe more massive person.

64. Two parallel conducting plates, separated by a distance d, areconnected to a battery of emf e. Which of the following is correctif the plate separaÂ¬tion is doubled while the battery remainsconnected?
(A) The electric charge on the plates is doubled.
(B) The electric charge on the plates is halved.
(C) The potential difference between the plates is doubled.
(D) The potential difference between the plates is halved
(E) The capacitance is unchanged.

68. A rod on a horizontal tabletop is pivoted at one end and isfree to rotate without friction about a vertical axis, as shownabove. A force F is applied at the other end, at an angle ? to therod. If F were to be applied perpendicular to the rod, at whatdistance from the axis should it be applied in order to proÂ¬ducethe same torque?
(A) L sin ? (B) L cos ? (C) L (D) L tan ? (E) L

70. A 4 ÂµF capacitor is charged to a potential differÂ¬ence of 100V. The electrical energy stored in the capacitor is
(A) 2 x 10-10 J (B) 2 x 10 8 J (C) 2 x 10 6 J (D) 2x 10-4 J (E) 2 x10-2 J

PHYS-2210 Study Guide - Final Guide: Root Mean Square, Ideal Gas, Ideal Gas Law

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYS-2210 Study Guide - Final Guide: Calorimetry, Isochoric Process, Thermodynamic Cycle

01:160:159 Study Guide - Midterm Guide: Effusion, Root Mean Square, Covalent Bond

CHEM 6B Lecture Notes - Lecture 6: Boiling Point, Compressibility Factor, Effusion

Related Questions