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Chapter 20: Q. 17 (page 567)

At what temperature (in°C)do hydrogen molecules have the same rms speed as nitrogen molecules at 100°C ?

Short Answer

Expert verified

The temperature of hydrogen molecules is-246°C

Step by step solution

01

Introduction

Equating the expressions for the rmsspeeds, we can find

3kBTnmn=3kBThmh

We can simplify the constants and raise the expression to the second power, thus obtaining

Tnmn=Thmh

It is therefore clear that the temperature of the hydrogen molecules will be

Th=Tnmhmn

02

Substitution 

Let us remember that the mass mof a molecule of a substance with molar mass Mwill be

m=MNA

Therefore it is clear that the ratio of molecular masses will be that of the molar masses,

mhmn=MhMn

Our final expression therefore becomes

Th=TnMhMn

Numerically we will have

Th=(100+273)228≈27K¯

In degrees Celsius, this temperature belongs to-246°C

03

Step 3:The Value of temperature

The temperature belongs to-246°C

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Most popular questions from this chapter

Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each container every second. In 10,000s, you find 80times when all the balls were in one container (either one) and the other container was empty.

a. How many balls are there?

b. What is the most likely number of balls to be found in one of the containers?

Dust particles are10μmin diameter. They are pulverized rock, with ρ≈2500kg/m3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at20°C?

By what factor does the rmsspeed of a molecule change if the temperature is increased from 10°C to 1000°C?

a. Find an expression for thevrmsof gas molecules in terms ofp,Vand the total mass of the gas M.

b. A gas cylinder has a piston at one end that is moving outward at speed vpistonduring an isobaric expansion of the gas. Find an expression for the rate at which is changing in terms of vpiston, the instantaneous value of vrms, and the instantaneous value Lof the length of the cylinder.

c. A cylindrical sample chamber has a piston moving outward at 0.50m/sduring an isobaric expansion. The rms speed of the gas molecules is localid="1648640672000" 450m/sat the instant the chamber length is localid="1648640676590" 1.5m. At what rate is localid="1648640708264" vrmschanging?

A mad engineer builds a cube,2.5mon a side, in which 6.2-cmdiameterrubber balls are constantly sent flying in random directions by vibrating walls. He will award a prize to anyone who can figure out how many balls are in the cube without entering it or taking out any of the balls. You decide to shoot 6.2-cmdiameter plastic balls into the cube, through a small hole, to see how far they get before colliding with a rubber ball. After many shots, you find they travel an average distance of 1.8m. How many rubber balls do you think are in the cube?
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