2) Operating a steady-state, a well insulated mixing chamber receives two input liquid streams of the same substance but with temperatures T1 and T2 and mass flow rates m ̇ 1 and m ̇ 2 respectively. The streams are mixed in the chamber, exiting as a single stream with T3 and m ̇ 3. Assuming the substance is incompressible with constant specific heat C, that potential energy, kinetic energy, and pressure changes are negligible, obtain an expression for

a) T3 in terms of T1, T2 and the ratio of the mass flow rates m ̇ 1/m ̇ 3.

b) the rate of entropy production per unit mass exiting the chamber in terms of C, T1/T2 and m ̇ 1/m ̇ 3.

c) For fixed values of C and T1/T2, determine the value for m ̇ 1/m ̇ 3 for which the rate of entropy production per unit mass out, σ ̇/m ̇3, is a maximum. (Hint start with an expression for σ ̇/m ̇3 as a function of m ̇ 1/m ̇ 3.)

NOTE: m * = M (Dot)

A 2290 kg car traveling at 11.7 m/s collides with a 2620 kg car that is initially at rest at the stoplight. The cars stick together and move 3.30 m before friction causes them to stop. Determine the coefficient of kinetic friction betwen the cars and the road, assuming that the negative acceleration is constant and that all wheels on both cars lock at the time of impact.

When you shine a laser with unknown wavelength through a diffraction grating with 1000 slits/mm, you observe the m = 1 bright fringe on the screen with an angle of 26 degrees away from the center of the grating.

What is the wavelength of your laser?

Plug in the relevant numbers to solve for your laser pointer photon wavelength in nanometers.

If the new diffraction bright fringe is at a LARGER angle than the diffraction bright fringe from the first grating, is the new diffraction spacing larger or smaller than the old diffraction line spacing?

Similarly, what if the new diffraction bright fringe is at a SMALLER angle?

1-History

a-In 2-3 sentences, describe the contributions of Emilie du Chatelet to physics.
b-What did Robert Hooke contribute to physics?
c-Who is your favorite physics person of history, and what did they do?
d-Compare and contrast the motion theories of Isaac Newton and Galileo Galilei. Be sure to point out places where each scientist was correct, as well as areas where they were not correct.

An atom in a 3d state emits a photon of wavelength 475.082 nm when it decays to a 2p state. (a) What is the energy (in electron volts) of the photon emitted in this transition? (b) Use the selection rules described in Section 41.4 to find the allowed transitions if the atom is now in an external magnetic field of 3.500 T. Ignore the effects of the electron’s spin. (c) For the case in part (b), if the energy of the 3d state was originally 8.50000 eV with no magnetic field present, what will be the energies of the states into which it splits in the magnetic field? (d) What are the allowed wavelengths of the light emitted during transition in part (b)?

Why is the cosmic star formation history peaking at redshift around 2? Hint: think of which processes are more (or less) active before (or after).

what do the shubnikov-de hass oscillations describe? draw the magnetoresistance

(a) Explain the Meissner effect of flux expulsion in a long superconducting wire arranged with its axis parallel to a magnetic field using the differential form of Faraday law of electromagnetie induetion. (b) Illustrate that the supereonductor not only excludes external magnetic field, it expels fields that has been established inside the superconductor using the graphical way such as B vs. H plot.

An object is placed in front of a lens with focal length f₁, a second lens is placed at a distance of d from the first lens and has focal length f₂. Given that the object has a height of h, find the height of the final image.

Describe a non-deterministic two-tape TM for testing whetehr the string on the first tape is a substring of the string in the second a tape. choose your own test cases

Given the angle of incidence and the angle of refraction, in a material of index of refraction n, find the speed of light in the material.

A particular HeNe laser operating at 632.8 nm has a tube that is 40 cm long. The operating gas temperature is about 130 C.

Calculate the frequency separation and the wavelength separation of the laser modes. How do these change as the tube warms up during operation? Taking the linear expansion coefficient to be 10-6 K-1, estimate the change in the mode frequency separation.

(please calculate the frequency separation and the wavelength separation)

In 2008, S. Stephen-Wales from Canada set the world record for his age group (15-19) for climbing the 320 m vertical height empire state building stairs. Suppose that he climbed the first 300 m in 12 minutes 30 seconds. Estimate the total power his body needed to produce in climbing the 300m if his body's bio-mechanical efficiency was 25%. Assume that his mass was 50kg.

Sam, whose mass is 70kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 280N and a coefficient of kinetic friction on snow of 0.15. Unfortunately, the skis run out of fuel after only 12s .How far has Sam traveled when he finally coasts to a stop?