Im trying to derive Cp - Cv = R where Cp and Cv are the molar specific heats at constant pressure and volume respectively. (R = 8.314 J/(mol*K)). So I'm only having problems with the last step.

I get that for a process at constant pressure we have:

∆E(internal) = Q + W = nCp∆T - P∆V

And I get that for a process at constant volume we have:

∆E(internal) = Q + W = Q + 0 => ∆E(internal) = Q

The last step is setting these two equations equal to one another, but I don't understand how we know that the internal energy of both processes are the same.

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.47 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) a)If a helium nucleus scatters to an angle of 108° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. b)What is the final kinetic energy (in J) of the helium nucleus?

A Light of wavelength 650 nm falls on two slits and produces an interference pattern in which the third-order bright red fringe is 47 mm from the central fringe on a screen 1.4 m away.

What is the separation of the two slits?

B In a double-slit experiment, the third-order maximum for light of wavelength 520 nm is located 17 mm from the central bright spot on a screen 1.6 m from the slits. Light of wavelength 630 nm is then projected through the same slits. How far from the central bright spot will the second-order maximum of this light be located?

C Light of wavelength 620 nm falls on a slit that is 3.70×10⁻³ mm wide. How far the first bright diffraction fringe is from the strong central maximum if the screen is 10.5 m away.

D A grating that has 3900 slits per cm produces a third-order fringe at a 27.0 ∘ angle.

What wavelength of light is being used?

E Red laser light from a He-Ne laser (λ = 632.8 nm) creates a second-order fringe at 53.2∘ after passing through the grating. What is the wavelength λ of light that creates a first-order fringe at 22.0 ∘ ?

F Light of wavelength 670 nm passes through two narrow slits 0.65 mm apart. The screen is 2.40 m away. A second source of unknown wavelength produces its second-order fringe 1.21 mm closer to the central maximum than the 670 nm light. What is the wavelength of the unknown light?

In the drawing, the rope and the pulleys are massless, and there is no friction. The larger block has a mass of 10.03kg and the smaller block has a mass of 3.85kg.

A spaceship leaves the earth, starting from rest and accelerating at a constance rate of 10m/s^2. its destination is the Moon, 380,000 km from earth. ignore size of earth and moon. Assume that both are at rest.

a.) At this rate of acceleration how long will it take the spacecraft to reach the moon?

for part b assume the spaceship accelerates to a halfway point (same acceleration as a)and then begins to deccelerate to have a final velocity of 0 when it reaches the moon.

b.) With the new method how long will it take for the spaceship to reach the moon?

the spaceship is carrying a probe which it can launch ouot of the front end of the spacecraft with a speed of 5000 m/s with respect to the spaceship.

c.) Assume the spaceship is traveling the same way as part b, at what distance from the moon should the probe be launched so that it will reach the moon at the same time as the saceship?

suppose the spaceship also has a probe that it can launch in the backward direction at the same speed of 5000 m/s with respect to the ship.

d.) In this case what distance from the moon should the probe be launched so that it will reach the moon at the same time as the ship?

Need to know how to do this type of work for my exam. An explained answer so i can follow along is greatly appreciated thank you in advance.

(1) A 190-kg object and a 490-kg object are separated by 4.40 m.

(a) Find the magnitude of the net gravitational force exerted by these objects on a 63.0-kg object placed midway between them. [N]

(b) At what position (other than an infinitely remote one) can the 63.0-kg object be placed so as to experience a net force of zero from the other two objects? [m from the 490 kg mass toward the 190 kg mass ]

(2)

(a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit? [km/s]

(b) Voyager 1 achieved a maximum speed of 125,000 km/h on its way to photograph Jupiter. Beyond what distance from the Sun is this speed sufficient to escape the solar system? [m]

I really need help with these 2 questions! Just need a final answer, little explanation required but please include the numerical work so I can understand and also please follow the units in the [brackets]

A) Determine the acceleration of a 25.0 kg mass down a frictionless incline plane (angle of incline=30 degrees)

B) Repeat the above problem for an incline with a coefficient of friction of 0.15.

1. About time intervals statistics,

   1. (a) A municipal bus system, when operating perfectly on schedule, provides a bus at any given bus stop every 30 min. You arrive at a random time at a bus stop. What is the average waiting time until the next bus arrives?

   2. (b) The busses become totally disorganized so that the spacing between busses is made random (assume that their arrival is a Poisson random process.) The same number of busses are still in operation. You again arrive at a bus stop at an arbitrary time. What is the average waiting time under these circumstances?

A conducting metallic spherical shell of inner radius a and outer radius b has a net positive charge Q on it. Using Gauss' law, calculate the electric field for the three regions defined by the shell: a) For r<z b) For a<r<b (inside shell) c) For r>b d) If we place a negative point -q at the center of the spherical shell, how would your answers to (a), (b), and (c) change? Calculate and explain.

Please explain answer...I want to understand the concepts used. Thank you in advance...I will rate.

Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about magnetic monopoles?

And more generally, why do we like gauge potentials so much?

A particle carrying charge +q is located on the xaxis at x=+d. A particle carrying charge ?3q is located on the x axis at x=?7d.

A. With zero potential at infinity, at what location on the x axis with negative coordinate is the electrostatic potential zero? Express your answer in terms of d.

B. With zero potential at infinity, at what location on the x axis with positive coordinate is the electrostatic potential zero? Express your answer in terms of d.

C. At what location on the y axis with negative coordinate is the potential zero? Express your answer in terms of d.

D. At what location on the y axis with positive coordinate is the potential zero? Express your answer in terms of d.

E. Are there any locations on the x or y axis where the electrostatic potential is zero?

A)How long (in ns) does it take light to travel 1.00

m in vacuum?

B) What distance does light travel in water during the time that it travels 1.00

m in vacuum?

C) What distance does light travel in glass during the time that it travels 1.00

m in vacuum?

A projectile is fired with an initial speed of 36.4 m/s at an angle of 43.0 ∘ above the horizontal on a long flat firing range.

A) Determine the maximum height reached by the projectile.

B) Determine the total time in the air.

C) Determine the total horizontal distance covered (that is, the range).

D)Determine the speed of the projectile 1.50 s after firing.

Background

As seen on this picture of the cosmic microwave background (take from the Wikipedia entry on the very same topic) there exists irregularities in the distribution of matter: Cosmic microwave background. Boom baby!

To my knowledge, this is because the Universe wasn't formed with all the matter (or whatever you should call whatever existed right after the big bang) in a completely regular pattern (or if it was the case that anti-matter had this big fight with ordinary matter after the Big Bang, it's really not that important I guess), and I guess this is the reason why we have a highly diverse universe today, inhabited by galaxies, black holes, and Justin Bieber.
Question

What would the Universe look like if there were no irregularities in it from the get-go? Would we have a big massive black hole in the middle (if one even can talk about a middle), would the Big Bang never happen, or have I just misunderstood the whole thing, making my question completely nonsensical?

how does the specific heat of water compare with that of various metals? Why?