Translational Energy of Molecules and Vrms

AI Thread Summary
The discussion focuses on calculating the average (rms) speed of hydrogen molecules in a one-liter container at 200 K and 1 atm. The initial calculation yielded an rms speed of 1579.30 m/s, which was deemed incorrect as the expected answer is 1600 m/s. Participants clarify that the discrepancy is not due to rounding, as the provided multiple-choice options suggest a precise answer. It is recommended to select the closest value in a multiple-choice format. The conversation emphasizes the importance of accuracy in physics calculations, especially in exam settings.
1st1
Messages
22
Reaction score
0
1. A quantity of molecular hydrogen (H2) gas fills a one liter container at a temperature of 200 K and pressure of 1 atm.

What is the average (rms) speed of the molecules?

Homework Equations



KE_trans = 1/2 M<v^2>
Energy_trans = 3/2kT = 3/2RT
H2 = 2g/mol

The Attempt at a Solution



Assuming 1 mol of H2:
mass = .002kg

1/2 M<v^2> = 3/2RT
(.002kg)<v^2> = 3R(200K)
<v^2> = 2494200m/s
Vrms = sqrt(<v^2>) = 1579.30m/s

Which is wrong.
The correct answer is 1600m/s. (Not a rounding error.)

Can anyone help me?
Thanks!
 
Physics news on Phys.org
The answer is certainly rounded.

ehild
 
The reason I don't believe its rounded is because the options are:
(a) 16 m/s
(b) 74 m/s
(c) 274 m/s
(d) 1600 m/s
(e) 4570 m/s

So if it were rounded it would be rounded to 1580 and in my
physics exams they always give you the exact answer or really close to it.
 
You result is correct. Do you need to present your calculation, or just have to choose one value? If it is a multi-choice question mark the closest one.

ehild
 
Yea, its a multiple choice question.
Thanks for your help!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Dimensional Analysis: Forster Energy Transfer equation
Replies
2
Views
1K
What is the problem with the units in this state equation of a gas?
Replies
12
Views
2K
Hooke's Law using Potential Energy
Replies
21
Views
1K
Ratio between molecules having different speeds
Replies
2
Views
1K
Finding what fraction of molecules have speeds over a certain value
Replies
2
Views
5K
Average Kinetic Energy of molecules calculation
Replies
7
Views
1K
Finding slip-off angle for mass off of sphere?
Replies
7
Views
1K
Macro/ micro connections- pressure
Replies
1
Views
2K
Calculate the rms speed of one nitrogen molecule at 27 Celcius
Replies
16
Views
3K
RMS velocity of molecules in a mixture
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top