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Chapter 1: Q. 1.18 (page 13)

Calculate the rms speed of a nitrogen molecule at room temperature.

Short Answer

Expert verified

Root mean square speed is 515.9m/s.

Step by step solution

01

Given information

Gas is Nitrogen.

Temp = room temp = 25oC= 298 K

02

Explanation

The root mean square velocity is calculated as

v=3kTm............................(1)

where

T = temperature

k = Boltzmann constant

m = mass

Mass of Nitrogen is calculated as

m=28u=28×1.6×10-27kg=4.65×10-26kg

Boltzmann constant is =1.38×10-23m2kgs-2K-1

Substitute the values in equation (1), we get

v=3×(1.38×10-23m2kgs-2K-1)×(298K)4.65×10-26kgv=515.9ms-1

Root mean square speed is 515.9m/s.

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Most popular questions from this chapter

An ideal diatomic gas, in a cylinder with a movable piston, undergoes the rectangular cyclic process shown in the given figure.

Assume that the temperature is always such that rotational degrees of freedom are active, but vibrational modes are "frozen out." Also assume that the only type of work done on the gas is quasistatic compression-expansion work.

(a) For each of the four steps A through D, compute the work done on the gas, the heat added to the gas, and the change in the energy content of the gas. Express all answers in terms of P1,P2,V1,andV2. (Hint: Compute ΔUbefore Q, using the ideal gas law and the equipartition theorem.)

(b) Describe in words what is physically being done during each of the four steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed.

(c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly.

According to a standard reference table, the R value of a 3.5 inch-thick vertical air space (within a wall) is 1.0 R in English units), while the R value of a 3.5-inch thickness of fiberglass batting is 10.9. Calculate the R value of a 3.5-inch thickness of still air, then discuss whether these two numbers are reasonable. (Hint: These reference values include the effects of convection.)

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