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Chapter 1: Q.1.23 (page 17)

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.

Short Answer

Expert verified

The total thermal energy in a liter is for heliumU=151.987J and for airU=253.312J.

Step by step solution

01

Step 1. Given data.

A liter of helium at ambient temperature at the pressure of one atmosphere1atm=101325Pa.

02

Step 2. Explanation.

Whereas a monatomic gas, like helium, has only three translational degrees of freedom, it is the simplest instance.

U=f2NkT=32NkT

Thermal energy,

U=32NkT=32PV=32脳101325脳1脳10-3=151.987J

03

Step 3. Total thermal energy.

A rotation around the bond's axis isn't counted because it doesn't change the molecule's position.

f=5

U=f2NkT=52NkTU=52PV=52脳101325脳1脳10-3=253.312.J

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Most popular questions from this chapter

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?

Uranium has two common isotopes, with atomic masses of 238 and 235. one way to separate these isotopes is to combine the uranium with fluorine to make uranium hexafluoride gas, UF6, then exploit the difference in the average thermal speeds of molecules containing the different isotopes. Calculate the rms speed of each molecule at room temperature, and compare them.

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.

  1. Sketch a graph of pressure vs. volume for this process.
  2. Calculate the work done on the gas during this process, assuming that there are no 鈥渙ther鈥� types of work being done.
  3. Calculate the change in the helium鈥檚 energy content during this process.
  4. Calculate the amount of heat added to or removed from the helium during this process.
  5. Describe what you might do to cause the pressure to rise as the helium expands.

Suppose you open a bottle of perfume at one end of a room. Very roughly, how much time would pass before a person at the other end of the room could smell the perfume, if diffusion were the only transport mechanism? Do you think diffusion is the dominant transport mechanism in this situation?

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.)

(a) What is the final volume of this air after compression?

(b) How much work is done in compressing the air?

(c) If the temperature of the air is initially300K , what is the temperature after compression?
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