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An Introduction to Thermal Physics

Daniel V. Schroeder

Physics

1st Edition · 356 pages

ISBN: 9780201380279

Chapter 1: 1.18. (page 13)

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

Short Answer

Expert verified

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

Step by step solution

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

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Most popular questions from this chapter

A battery is connected in series to a resistor, which is immersed in water (to prepare a nice hot cup of tea). Would you classify the flow of energy from the battery to the resistor as "heat" or "work"? What about the flow of energy from the resistor to the water?

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?

In analogy with the thermal conductivity, derive an approximate formula for the diffusion coefficient of an ideal gas in terms of the mean free path and the average thermal speed. Evaluate your formula numerically for air at room temperature and atmospheric pressure, and compare to the experimental value quoted in the text. How does D depend on T, at fixed pressure?

A cup containing 200g of water is sitting on your dining room table. After carefully measuring its temperature to be 20^oC, you leave the room. Returning ten minutes later, you measure its temperature again and find that it is now 25^oC. What can you conclude about the amount of heat added to the water? (Hint: This is a trick question.)

If you poke a hole in a container full of gas, the gas will start leaking out. In this problem, you will make a rough estimate of the rate at which gas escapes through a hole. (This process is called effusion, at least when the hole is sufficiently small.)

Consider a small portion (area = $A$ ) of the inside wall of a container full of gas. Show that the number of molecules colliding with this surface in a time interval $Δ t$ is role="math" localid="1651729685802" $P A Δ t / (2 m \bar{v_{x}})$ , where width="12" height="19" role="math">Pis the pressure, is the average molecular mass, and $v_{x}$ is the average $x$ velocity of those molecules that collide with the wall.
It's not easy to calculate $v_{x}$ , but a good enough approximation is ${(\bar{v_{x}^{2}})}^{1 / 2}$ , where the bar now represents an average overall molecule in the gas. Show that ${(\bar{v_{x}^{2}})}^{1 / 2} = \sqrt{k T / m}$ .
If we now take away this small part of the wall of the container, the molecules that would have collided with it will instead escape through the hole. Assuming that nothing enters through the hole, show that the number $N$ of molecules inside the container as a function of time is governed by the differential equation
$\frac{d N}{d t} = - \frac{A}{2 V} \sqrt{\frac{k T}{m} N}$
Solve this equation (assuming constant temperature) to obtain a formula of the form $N (t) = N (0) e^{- t / r}$ , where $r$ is the “characteristic time” for $N$ (and $P$ ) to drop by a factor of $e$ .
Calculate the characteristic time for gas to escape from a 1-liter container punctured by a $1 - {mm}^{2}$ ? hole.
Your bicycle tire has a slow leak so that it goes flat within about an hour after being inflated. Roughly how big is the hole? (Use any reasonable estimate for the volume of the tire.)
In Jules Verne’s Around the Moon, the space travelers dispose of a dog's corpse by quickly opening a window, tossing it out, and closing the window. Do you think they can do this quickly enough to prevent a significant amount of air from escaping? Justify your answer with some rough estimates and calculations.

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

Short Answer

Step by step solution

Arriving at rms speed by substituting the data ,

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