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Chapter 1: Q 1.63 (page 44)

At about what pressure would the mean free path of an air molecule at room temperature equal 10cm, the size of a typical laboratory apparatus?

Short Answer

Expert verified

The mean free path pressure is P=0.146N⋅m−2

Step by step solution

01

Step: 1 To find pressure of mean free path:

The equation as

PV=NKT

V=π(2γ)2ℓ

By equating,

P=UT4πγ2λ

02

Subtituting the values 

subtituting the values of

T=100dr,γ=0.01,P=0.082N/m2as

P=1.381×10−23×1004π×2×10−102×0.01

P=0.274Nm2.

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Most popular questions from this chapter

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?

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.

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

Determine the Kelvin temperature for each of the following:

(a) human body temperature;

(b) the boiling point of water(at the standard pressure of 1 atm);

(c) the coldest day u can remember;

(d) the boiling point of liquid nitrogen(-196°C);

(e) the melting point of lead(327°C)

Two identical bubbles of gas form at the bottom of a lake, then rise to the surface. Because the pressure is much lower at the surface than at the bottom, both bubbles expand as they rise. However, bubble A rises very quickly, so that no heat is exchanged between it and the water. Meanwhile, bubble B rises slowly (impeded by a tangle of seaweed), so that it always remains in thermal equilibrium with the water (which has the same temperature everywhere). Which of the two bubbles is larger by the time they reach the surface? Explain your reasoning fully.

By applying a pressure of 200atm, you can compress water to 99%of its usual volume. Sketch this process (not necessarily to scale) on aPV diagram, and estimate the work required to compress a liter of water by this amount. Does the result surprise you?
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