Kinetic theory problems: raindrops, gas speeds, and adiabatic expansion

[tido_29]

Kinetic theory HW help :(

I am new here and found the site while trying to find a formula. I am having problems solving some questions. I worked out what i could but don't know if i did it right. Please Help :(

PROBLEM 1

A raindrop of mass (1mg) fall vertically at a constant speed of 10 m/s, striking a horizontal skylight at the rate of 1000 drops/s and draining off. The window is 15cm X 25cm. Assume the collisions are completely inelastic.

a) Calculate the magnitude of the average force of the raindrops on the window.

i used this equation. F(ave) = -2mV/(2L/V)

-2(1x10^-6kg)(10m/s) / ( 2 (.0375m^2)/(10m/s) ) = 2.66x10^-3 (is this right?)

b) what is the resuling pressure developed by the raindrop.

I know that P= F(average)/Area I know the area and F(average) is from above.



PROBLEM 2

The molar mass of N2 is 28g.

a) find the mass of 1 nitrogen molecule.

(1mol N2/ 28g N2) X ( 6.02x10^23 molecules/ mol) = 2.15x10^25 mol/g so each molecule weighs (the inverse) = 4.65x10^-23g

b) Find the rms speed of a nitrogen molecule at a temp. of -23C.
V(rms) = (3RT/M)^.5

( (3*8.315*250.15K)/ 28g ) ^.5 = 14.9

c) H2 is also present in same container. molar mass 2g/mol. What is the temp of the Hydrogen gas?

This is where I am stuck ? do i use the PV= nRT

D) what is the rms speed of the hydrogen molecule?

I used the V(rms) = 3RT/M (the T is what i am trying to find from part C right?

e) what new temp would cause the V(rms) to increase by 2 in part b?
New temp = part b temp x 2. right? = 250.15K x 2 = 500.3K = 227.15C.


Problem 3

1 mol of HE gas @ 300K is in a cubical box of 10cm sides.

a) what is the Vrms of the particles.

V= 3RT/M ---> 3(8.315)(300) / 4.0026 = 43.23

b) If there were no collisins along the way, how long would it take a particle to travel from one side to the next?
L= Vt t(time)= L/v ----> .1meter/43.23 = 2.313x10^3 sec.

c) what is the pressure of the container?

PV= nRT solving to P---> P= nRT/V ( (1mol)(8.315)(300K) / 10m^3 ) = 249.45

d) what is the average force of the particle excerted on the side of the box?

F(ave) = MV^2 / L---------> ( (4.0026)(43.23m/s)^2 ) / (10m^3) = 7.48x10^4


Problem 4

1 mol of a monatomic ideal gas @ temp 300K accupies a volume of 5Litters. The gas now expands adiabatically till its volume is doubled. What is the final pressure of the gas? (NOTE : @ = gamma)

I am using the

PV^@ = constant.

Pfinal X Vfinal ^@ = Pinitial X Vinitial^@

solving for Pfinal... i get P(f) = P(i) X (V(i)/V(f))^@.

I found @ to be equal to 1.66 by the equations @ = C(p)/ C(v) where Cv = 3/2R and Cp = Cv + R.

so P(f) = .31498 X P(i) where P(i) = 498.9 from the PV= nRT

 

[M98Ranger]

and solving for P. P(i) = (1mol)(8.315)(300K)/(5L) = 498.9

What is the final pressure of the gas?



Thank you for your question and the detailed work you have shown in solving these problems. It seems like you have a good understanding of the concepts and equations involved in kinetic theory.

To answer your questions:

Problem 1
a) Your calculation for the average force seems correct. Good job!
b) To find the resulting pressure, you can use the formula you mentioned: P = F(ave)/Area. However, make sure to convert the area to square meters (0.0375 m^2 = 0.000375 m^2). Your final answer should be in Pascals (Pa).

Problem 2
a) Your calculation for the mass of one nitrogen molecule is correct.
b) Your calculation for the rms speed of a nitrogen molecule is also correct.
c) To find the temperature of the hydrogen gas, you can use the ideal gas law: PV = nRT. Since the volume and number of moles (1 mol) are the same for both gases, you can set the two equations (for N2 and H2) equal to each other and solve for T.
d) To find the rms speed of the hydrogen molecule, you can use the same equation as in part b), but with the temperature you found in part c).
e) Yes, your calculation for the new temperature is correct.

Problem 3
a) Your calculation for the rms speed is correct.
b) To find the time it takes for a particle to travel from one side to the next, you can use the equation t = L/v, but make sure to convert the length to meters (0.1 m). Your final answer should be in seconds (s).
c) Your calculation for the pressure is correct.
d) Your calculation for the average force is also correct.

Problem 4
Your approach for solving this problem is correct. Your final answer for the final pressure should be in Pascals (Pa).

Overall, you seem to have a good grasp on the concepts and equations involved in kinetic theory. Keep up the good work! If you have any further questions, don't hesitate to ask for help.