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1.18.

Expert-verified

Found in: Page 13

Book edition 1st

Author(s) Daniel V. Schroeder

Pages 356 pages

ISBN 9780201380279

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Short Answer

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

The rms speed of a nitrogen molecule at room temperature is 16.34 m/s

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 2 : Arriving at rms speed by substituting the data ,

Since we are recalculating for Nitrogen molecule the molar mass of N₂₌28

Substituting all the values ,

$V_{r m s} = \sqrt{\frac{3 \times 8.314 \times 300}{28}}$

V_rms=16.34m/s

Most popular questions for Physics Textbooks

Calculate the total thermal energy in a liter of helium at room temperature and atmospheric pressure. Then repeat the calculation for a liter of air.

Even at low density, real gases don’t quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial

expansion,

$P V - n R T (1 + \frac{B (T)}{(V / n)} + \frac{C (T)}{{(V / n)}^{2}} + \dots)$

where the functions $B (T)$ , $C (T)$ , and so on are called the virial coefficients. When the density of the gas is fairly low, so that the volume per mole is large, each term in the series is much smaller than the one before. In many situations, it’s sufficient to omit the third term and concentrate on the second, whose coefficient $B (T)$ is called the second virial coefficient (the first coefficient is 1). Here are some measured values of the second virial coefficient for nitrogen ( $N_{2}$ ):

$T (K)$	$B (c m^{3} / m o l)$
100	–160
200	–35
300	–4.2
400	9.0
500	16.9
600	21.3

For each temperature in the table, compute the second term in the virial equation, $B (T) / (V / n)$ , for nitrogen at atmospheric pressure. Discuss the validity of the ideal gas law under these conditions.
Think about the forces between molecules, and explain why we might expect $B (T)$ to be negative at low temperatures but positive at high temperatures.
Any proposed relation between $P$ , $V$ , and $T$ , like the ideal gas law or the virial equation, is called an equation of state. Another famous equation of state, which is qualitatively accurate even for dense fluids, is the van der Waals equation, $(P + \frac{a n^{2}}{V^{2}}) (V - n b) = n R T$ where a and b are constants that depend on the type of gas. Calculate the second and third virial coefficients ( $B$ and $C$ ) for a gas obeying the van der Waals equation, in terms of $a$ and $b$ . (Hint: The binomial expansion says that ${(1 + x)}^{p} \approx 1 + p x + \frac{1}{2} p (p - 1) x^{2}$ , provided that $| p x | ≪ 1$ . Apply this approximation to the quantity ${[1 - (n b / V)]}^{- 1}$ .)
Plot a graph of the van der Waals prediction for $B (T)$ , choosing $a$ and $b$ so as to approximately match the data given above for nitrogen. Discuss the accuracy of the van der Waals equation over this range of conditions. (The van der Waals equation is discussed much further in Section 5.3.)

Imagine some helium in a cylinder with an initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in direct proportion to its volume.

Sketch a graph of pressure vs. volume for this process.
Calculate the work done on the gas during this process, assuming that there are no “other” types of work being done.
Calculate the change in the helium’s energy content during this process.
Calculate the amount of heat added to or removed from the helium during this process.
Describe what you might do to cause the pressure to rise as the helium expands.

Problem 1.41. To measure the heat capacity of an object, all you usually have to do is put it in thermal contact with another object whose heat capacity you know. As an example, suppose that a chunk of metal is immersed in boiling water (100°C), then is quickly transferred into a Styrofoam cup containing 250 g of water at 20°C. After a minute or so, the temperature of the contents of the cup is 24°C. Assume that during this time no significant energy is transferred between the contents of the cup and the surroundings. The heat capacity of the cup itself is negligible.

How much heat is lost by the water?
How much heat is gained by the metal?
What is the heat capacity of this chunk of metal?
If the mass of the chunk of metal is 100 g, what is its specific heat capacity?

An ideal gas is made to undergo the cyclic process shown in the given figure. For each of the steps A, B, and C, determine whether each of the following is positive, negative, or zero: (a) the work done on the gas; (b) the change in the energy content of the gas; (c) the heat added to the gas.

Then determine the sign of each of these three quantities for the whole cycle. What does this process accomplish?

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Short Answer

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

Step by Step Solution

Step 2 : Arriving at rms speed by substituting the data ,

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

Step by Step Solution

Step 2 : Arriving at rms speed by substituting the data ,

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