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23 Nov 2019

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.

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

(a) How does kinetic-molecular theory explain the change in pressure when the volume of a sample of gas decreases while the temperature remains constant?

(b) How does kinetic-molecular theory explain the change in pressure when gas molecules are added to a sample of gas in a rigid container at constant temperature?

Three moles of oxygen gas (O2) are placed in a container with avolume of 0.0035 m3. If the temperature of the gas is 295oC A) Findthe pressure of the gas and the average kinetic energy of amolecule of the oxygen.
B) Suppose the volume of the gas is doubled while the temperatureand the number of moles are held constant, find the new pressureand average kinetic energy of a molecule

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 speedv_avgof 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 rootv_rms. The quantityv_rmsis 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 speedv_rmsof the molecules in the nitrogen gas?

Express your answer numerically to three significant digits.
Part C

What is the temperatureTof the sample of\rm N_2gas described in the histogram?

Express your answer in degrees Celsius to three significant figues.

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