7 please Activity 1: Counting Microstates and Calculating ProbabilitiesIf there is only one molecule of gas in the system (N=1), then there are 2 possible microstates forthe system. If N=2, there are 4 possible microstates. This becomes easy to see if you think of allthe possible ways to arrange the molecules and draw a diagram of each one, as shown below.N = 1N = 21. In the space below, draw a sketch of all possible microstates for N = 3. Use different shapesor different colors so you can tell the particles apart. You should work it out on scratch paperfirst. What is the total number of microstates?N= 32. In the space below, draw a sketch of all possible microstates for N = 4. What is the totalnumber of microstates?24 = 16.. 3. Can you see a pattern emerging? Come up with a general formula for the total number ofmicrostates for a system of N gas molecules. The only variable in your formula should be N.n=2N4. For each case we've sketched out (N = 1 to N = 4), how many microstates are there with allof the particles on the right side of the box? Does your answer depend on N?number of microstates with all molecules on the right side of the box =Does your answer depend on the number of molecules of gas in the system? Y/N5. Write down the formula for the probability of finding all of the gas molecules on the rightside of the box. Read the introduction section again if you're not sure how to do this. Theonly variable in your formula should be N.6. Suppose that the box contains 4 molecules. Use your formula to calculate the probability offinding all of the molecules on the right side of the box..062516247. Now suppose that the box contains 1023 gas molecules. Use your formula to calculate theprobability of finding all of the molecules on the right side of the box. Realistically, wouldyou ever expect to see this happen?

Answered: Image /qna-images/answer/78f4667c-28b0-411e-a694-34287f415504.jpg

7. Now suppose that the box contains 1023 gas molecules. Use your formula to calculate the probability of finding all of the molecules on the right side of the box. Realistically, would you ever expect to see this happen?

7. Now suppose that the box contains 1023 gas molecules. Use your formula to calculate the probability of finding all of the molecules on the right side of the box. Realistically, would you ever expect to see this happen?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter31: Radioactivity And Nuclear Physics

Section: Chapter Questions

Problem 3PE: (a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is...

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Concept explainers

Kinetic Theory of Gas

The Kinetic Theory of gases is a classical model of gases, according to which gases are composed of molecules/particles that are in random motion. While undergoing this random motion, kinetic energy in molecules can assume random velocity across all directions. It also says that the constituent particles/molecules undergo elastic collision, which means that the total kinetic energy remains constant before and after the collision. The average kinetic energy of the particles also determines the pressure of the gas.

P-V Diagram

A P-V diagram is a very important tool of the branch of physics known as thermodynamics, which is used to analyze the working and hence the efficiency of thermodynamic engines. As the name suggests, it is used to measure the changes in pressure (P) and volume (V) corresponding to the thermodynamic system under study. The P-V diagram is used as an indicator diagram to control the given thermodynamic system.

Question

7 please

Activity 1: Counting Microstates and Calculating Probabilities
If there is only one molecule of gas in the system (N=1), then there are 2 possible microstates for
the system. If N=2, there are 4 possible microstates. This becomes easy to see if you think of all
the possible ways to arrange the molecules and draw a diagram of each one, as shown below.
N = 1
N = 2
1. In the space below, draw a sketch of all possible microstates for N = 3. Use different shapes
or different colors so you can tell the particles apart. You should work it out on scratch paper
first. What is the total number of microstates?
N= 3
2. In the space below, draw a sketch of all possible microstates for N = 4. What is the total
number of microstates?
24 = 16
..

3. Can you see a pattern emerging? Come up with a general formula for the total number of
microstates for a system of N gas molecules. The only variable in your formula should be N.
n=2N
4. For each case we've sketched out (N = 1 to N = 4), how many microstates are there with all
of the particles on the right side of the box? Does your answer depend on N?
number of microstates with all molecules on the right side of the box =
Does your answer depend on the number of molecules of gas in the system? Y/N
5. Write down the formula for the probability of finding all of the gas molecules on the right
side of the box. Read the introduction section again if you're not sure how to do this. The
only variable in your formula should be N.
6. Suppose that the box contains 4 molecules. Use your formula to calculate the probability of
finding all of the molecules on the right side of the box.
.0625
16
24
7. Now suppose that the box contains 1023 gas molecules. Use your formula to calculate the
probability of finding all of the molecules on the right side of the box. Realistically, would
you ever expect to see this happen?

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