Question

A helium-4 atom falls from a height h into a tank of gaseous helium atoms at 300 K. What is h in meters if the temperature of the helium atoms remains at 300 K after the falling atom enters the tank?

Details and assumptions
The acceleration of gravity is −9.8 m/s2.
As the atom falls it is in vacuum.
The atom starts from rest.

please help

Answer 1

how should i approach this problem

Answer 2

consider helium to be like stone OK

Answer 3

since its falling on the earth g=*9.8

Answer 4

4 helium atoms are there or only one Helium atom is there

Answer 5

helium 4 means the mass number 2 proton and 2 electrons

Answer 6

ok then you got the mass of the stone too

Answer 7

THis it was initially at rest it was at 0k,then mgh=mcT

Answer 8

mass isn't given it should be done based on the assumption above

Answer 9

yaaa mass u take as 4 gram ok

Answer 10

what is McT

Answer 11

it is the formula fo heat transfer,m is mass,c is specific heat capacity and t is the temperature,the mgh=mct ,gh=ct,
i have no idea how to get the specific heat capacity,

Answer 12

they have asked to find the height dude why are you relating to specific heat capacity

Answer 13

because there is a temperature change from 0k to 300k.the mass isn't given

Answer 14

and mechanical work causes a change in temperature

Answer 15

they have given constant temperature of 300 K LOL:)

Answer 16

the rms velocity of an atom is given by
\[v=\sqrt{3RT/M}\]
R=gas constant
T=temperature
M=molar mass
For helium M = 4 grams
and it is given that it enters with such velocity that its temperature is 300K. We can thus know the velocity. Hence the kinetic energy which was initially stored as potential energy.
Apply conservation of mechanical energy and find h.

Answer 17

mgh =mvh ????or what

Answer 18

mgh = mv^2/2
where v is the velocity we found from above formula

Answer 19

ok ok i was getting trouble to correlate the right side term any way thank you

Answer 20

a single atom can not weigh 4 grams,

Answer 21

h=v^2/2g

Answer 22

no.if an atom is at rest,it means it is at 0k,absolute zero

Answer 23

LOL:( no its not OK K is unit of temperature how can you relate this too rest

Answer 24

is 11.47 correct ?

Answer 25

because absolute zero is the temperature at which there is no vibration or movement,hence no kinetic energy

Answer 26

in this case m will cancel and not needed LOL:)

Answer 27

how do u get 11.47

Answer 28

so what's the answer ?

Answer 29

V2/2g

Answer 30

i equated the K.E. and the P.E. taking m = 4 grams ! is it correct ?

Answer 31

no,4 grams is way to big for a single atom

Answer 32

so now what is the correct answer ?

Answer 33

just solve the square root of 3RT/M putting T =300K ,M=4 , R=8.314

Answer 34

that will give the rms velocity not height !

Answer 35

Q=mct,where m is the mass,c is heat capacity and t is change in temperature.
where q = mgh
thus mgh=mct,which m cancels out,and it simplify it to h 300c/9.8, c=3/2r for monoatomic gases

Answer 36

v=43.25 next find the h

Answer 37

h=V2/2g

Answer 38

95.40 meters

Answer 39

if r= 3/2r where r is gas constant,so h = 300*3/9.8*2r