1 Ideal Gas Law The ideal gas law is familiar to anyone who has taken a college chemistry course: P V = νRT. This problem will show you why the ideal gas law has this form. We can arrive at this expression just by using classical mechanics! Consider a box of volume V containing N particles, each having mass m, that are moving horizontally with average speed v. The particles bounce back and forth between the end walls of the container, which have area A. They are spread out uniformly in the box, so that there are n = N/V particles per cubic meter.

Single Collision — Consider a single particle bouncing off a wall of the container. In an elastic collision, how much momentum is transferred to the wall of the container? (The wall has a much greater mass than a particle.)

Multiple Collisions — If there are N collisions like the one you analyzed in the preceding question, how much momentum will be transferred to the wall? Time Interval — How many collisions will occur in time ∆t? Express your result N in terms of the average speed v, the particle density n, the area of the wall A, and the time interval ∆t. (Remember: At any given time, only half the particles will be moving toward the wall; the other half will be moving away.)

Average Force — What is the average force on the wall due to the N collisions of the previous question? (Recall Newton’s Second Law: F = ∆p/∆t.)

Average Pressure — What is the average pressure on the wall?

Kinetic Energy — Rewrite your result in terms of the average kinetic energy of the particles: E = 1/ 2mv^2 .

Ideal Gas Law? — Rearrange your result to resemble the ideal gas law. That is, derive an expression that relates P, V , N, and E.

Average Energy — What value of the average energy E would give the physicists’ version of the ideal gas law, P V = N kBT?

In matlab I have created the following function that calculates the distance a projectile travels when shot from
a cannon given initial velocity and theta.

function [distance, xplot, yplot] = Cannon_lab8(V, theta)

g = -9.81; % gravity m/s^2
k = 0.35; % drag coefficient
Vx = V*cos(theta); %velovity in x-direction
Vy = V*sin(theta); %velovity in y-direction
dt = 0.01; % seconds, time step
x = 0;
y = 0;
xplot(1) = 0;
yplot(1) = 0;
i = 2;

while y >= 0
ax = -k*Vx;
ay = -k*Vy + g;
Vix = Vx;
Viy = Vy;
Vx = Vx + ax*dt;
Vy = Vy + ay*dt;
Vx_avg = (Vix +Vx)/2;
Vy_avg = (Viy +Vy)/2;
dy = Vy_avg * dt;
dx = Vx_avg * dt;
y = y + dy;
x = x +dx;
xplot(i) = x;
yplot(i) = y;
i = i + 1;
end

distance = x; % meters

scatter(xplot,yplot)
axis equal

I am now trying to determine the theta value needed to hit a target. The general aproach to solving for theta is by creating a new function that takes the guess value of theta, the initial velocity, and target distance, and solves for theta needed to hit the target. In this function the distance that the cannon misses the taret by can be calculated and this can be repeaditly calculated until the miss is within 2. so far I have:  

function [theta_target] = aim_lab9(theta_guess, target, V)
miss = Cannon_lab8(V, theta) - target;
dtheta = 0.1;
while abs(miss) > 2
miss = Cannon_lab8(V, theta_guess) - target;   
theta_new = theta_guess + dtheta;
miss2 = Cannon_lab8(V,theta_new) - target;
end

I need help determining the theta_target. I would also like for the code to check and see if the target is within range.

thank you!

python program

You are going to write a program that takes two inputs: A string representing a list of names of the following form: first name 1, last name 1, (nick name 1); first name 2, last name 2, (nick name 2); ... A string representing part of or the complete family name. You are going to output all nick names for those names where there is a partial or complete match of the family name. If no match was found you should output: Not found! Here a few examples.

Names: Chun Kit, Chui (Kit gor); Dirk, Schnieders (Dirk); Jun-fan, Lee (Bruce); Rowan Sebastian, Atkinson (Bean)

Family name: Schni

Dirk

In the circuit of Figure P32.48, the battery emf is 80 V, the resistance R is 240 , and the capacitance C is 0.500 µF. The switch S is closed for a long time, and no voltage is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance L?

The following groups are stakeholders of a public company:I) shareholders; II) the government; III) suppliers; IV) employees; V) bondholders; VI) management Select one:

a. I, II, III, IV, V, and VI

b. I and II only c. I, II, III, and IV only

d. I, II, and III only

Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = C ∞[0, 1] spanned by f(x) = 1, g(x) = x, and h(x) = e x where V has the inner product defined by < f, g >= R 1 0 f(x)g(x)dx.

A particle with mass m and energy E is moving in one-dimension from right to legt. It is incident on the step potential V(x)=0 for x<0 nd V(x)=V0 for x>0 where E>V0>0. Find the reflection coefficient R in terms of m,E and V0, and h-bar.

Use the postulates of the kinetic moleclar theory (KMT) to explain why boyle's law, charles's law, avogadro's law, and dalton's law of partial pressures hold true for ideal gases. Use the KMT to explain the P versus n (at constant V and T) relationship and the P versus T (at constant V and n) relationship.

1. Explain how an automatic pipette (like the one pictured) below works. Briefly explain how to use it
2. How can you accurately aliquot a highly viscous solution using an automatic pipette?
3. What does the term “specific gravity” mean? What is the specific gravity of a 50% (v/v) ethanol (in water) solution?

Calculate the amount of solution (g or mL) that contains each of the following amounts of solute.

5.2 g of LiNO3 from a 35 %(m/m) LiNO3 solution.

31.6 g of KOH from a 20.0 %(m/m) KOH solution.

3.1 mL of formic acid from a 18 %(v/v) formic acid solution.