Macro/ micro connections- pressure

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AI Thread Summary
The discussion focuses on estimating the number of nitrogen gas molecules in a cube at specified conditions. The initial calculations using the formula N = 3PV/(mv²rms) yield an unexpected result of 0.024 molecules, prompting concerns about accuracy. Participants suggest that the Maxwell-Boltzmann distribution should be applied to obtain a more accurate estimate of the number of molecules with speeds between 700 m/s and 1000 m/s. The conversation highlights the importance of using the correct statistical mechanics principles for gas behavior. Overall, the need for a more refined approach to the problem is emphasized.
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Homework Statement


A 1.3m×1.3m×1.3m cube of nitrogen gas is at 20∘C and 1.5 atm. Estimate the number of molecules in the cube with a speed between 700 m/s and 1000 m/s.

Homework Equations


P= (1/3) (N/V) (Mv2rms)

The Attempt at a Solution


20oc = 293 K
1.5 atm = 151950 Pa

Solving for N
N= 3PV/(mv2rms)

N= 3(151950)(2.197) / (28 x 12202)
N= 0.024 Molecules ?
This doesn't seem right?
 
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It looks like you need to use the Maxwell- Boltzmann distribution for this.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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