An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 6.4, Problem 36P
To determine
The average speed of an ideal gas.
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Write the Ideal gas law in terms of molecules?
In the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10
a) 2.1*10-7 m
b) 4.2*10-7 m
c) none of these.
What are the different ways of increasing the number of molecular collisions per unit time in a gas?
Chapter 6 Solutions
An Introduction to Thermal Physics
Ch. 6.1 - Prob. 2PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12P
Ch. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - For an O2 molecule the constant is approximately...Ch. 6.2 - The analysis of this section applies also to...Ch. 6.3 - Prob. 31PCh. 6.4 - Calculate the most probable speed, average speed,...Ch. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.4 - Prob. 39PCh. 6.4 - Prob. 40PCh. 6.5 - Prob. 42PCh. 6.5 - Some advanced textbooks define entropy by the...Ch. 6.6 - Prob. 44PCh. 6.7 - Prob. 45PCh. 6.7 - Equations 6.92 and 6.93 for the entropy and...Ch. 6.7 - Prob. 47PCh. 6.7 - For a diatomic gas near room temperature, the...Ch. 6.7 - Prob. 49PCh. 6.7 - Prob. 50PCh. 6.7 - Prob. 51PCh. 6.7 - Prob. 52PCh. 6.7 - Prob. 53P
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- An ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?arrow_forwardIn the text, it was shown that N/V=2.681025m3 for gas at STP. (a) Show that this quantity is equivalent to N/V=2.681019cm3, as stated. (b) About how many atoms are mere in one m3 (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of Mama and molecules?arrow_forwardAn ideal gas is confined to a container whose volume is fixed. If the container holds n moles of gas, by what factor will the pressure increase if the absolute temperature is increased by a factor of 2?arrow_forward
- Given the ideal gas law P V = k T, where k> 0 is a constant. We have the equation for V in terms of P and T. Finding the rate of change of the volume with respect to temperature at constant pressure, the interpretation of the result is: 1 Because this partial derivative is negative, the volume decreases as the temperature decreases at a fixed pressure. . 2. Because this partial derivative is negative, the volume increases as the temperature increases at a fixed pressure. 3. Because this partial derivative is positive, the volume increases as the temperature decreases at a fixed pressure. 4. Because this partial derivative is positive, the volume increases as the temperature increases at a fixed pressure.arrow_forwardHow is momentum related to the pressure exerted by a gas? Explain on the molecular level, considering the behavior of molecules?arrow_forwardProblem 1.18. Calculate the rms speed of a nitrogen molecule at room temperature.arrow_forward
- What is the average kinetic energy of a nitrogen molecule (N2) if its rms speed is 560 m/s? At what temperature is this rms speed achieved?arrow_forwardThe mean free path for a certain gas is 2.18×10−7 m. and the radius of an atom of said gas is approximately 1.11×10−11 m. What is the density of the gas in moles per cubic meter under these conditions?arrow_forwardAn ideal gas is confined to a container at a temperature of 330 K. 1)What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.)arrow_forward
- Use the Maxwell distribution to calculate the average value of v2 for the molecules in an ideal gas. Check that your answer agrees with equation 6.41 (Attached).arrow_forwardIn a gas that is a mixture of water (two H and one O) and carbon dioxide (one C and two O), if the water has average velocity of 347 m/s, what is the average velocity of the carbon dioxide molecule? Give your answer as number in units of m/s without entering the units.arrow_forwardHow many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.arrow_forward
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