That Thang

The allowed magnitudes of angular momentum are L = h ( l ( l + 1 ) ) ^ ( 1 / 2 ). Use the binomial expansion to prove that when l is large, L = h(l + 1/2).

Water (Cp=4180 J/kg K) is to be heated by solar heated hot air (Cp=1010J/kg K) in a double pipe countercurrent flow heat exchanger. Air enters the heat exchanger at 90 C at a rate of 0.3 kg/s, while water enters at 22 C at a rate of 0.1 kg/s. The overall heat transfer coefficient based on the inner side of the tube is 80 W/m2 K. The length of the tube is 12 m with internal diameter of 1.2 cm. Determine the outlet temperatures of the water and air.

What are the energy and wavelength of photons in the Lyman alpha line of Fe 25+(an iron nucleus with all but one of its 26 electrons removed)?

The formulas for the deflection of an electron in an electric or magnetic field are quite similar. Explain in words why both formulas have factors of v in the denominator and why the magnetic deflection has just one power of v where the electric has two.

θ = eEl/(mv^2) --> angle of deflection of an electron traveling in the positive x direction with an electric field pointing in the positive y direction

θ = eBl/(mv) --> angle of deflection of an electron traveling in the positive x direction with a magnetic field pointing in the z direction

I'm assuming in the electric field, the electron is accelerating, thus v is squared. But I'm not sure why the velocity term is in the denominator.

At what pressure would the density of He gas at T = 300 K equal the density of ordinary water? Density of water = 1kg/L

A star is receding from us at 0.5c. What is the percent shift in the frequency of light received from the star?

There is a steady leak of air into the tank at a rate of 0.001 Lbm/min. The furnace contains a total volume of 10 ft^3 of air, which may be considered an ideal gas. The vacuum pump is pumping air out prior to beginning the thermal diffusion step. During the pumpout process the heating coils in the tank hold the temperature in the tank constant at 68F. The volumetric flow rate at the inlet of the pump, independent of pressure, is 1.0 ft3/min. Calculate the final pressure of the system after 60 minutes assuming initial pressure of 1 atm.

In March 1996 a special release of water, Q = 45,000 ft^3/s, was made from the Glen Canyon Dam, to create an artificial flood in the Grand Canyon. The flow was through 8 pipes, each with an internal diameter of 8 ft. Estimate the velocity through those pipes. Estimate the average velocity of the river at some point downstream of the dam, where the width of the river was 200 ft and its average depth was 10 ft.

1000 kg of a 20percent by wt mixture of acetone in water is separated by multistage batch distillation. The top product (distillate) contains 95percent by wt. acetone and the still contains 2percent acetone. Calculate the amount of distillate.

(-1)^n * u(t-n) where u(t-n) is the step function.

1) A is a 8x8 matrix and dim(Row(A^T)) = 6

2) A is a 7x5 matrix in which dim(Null(A^T)) = 3

x''+w^2x = cos(w1t)

x(0)=x'(0)=0

w and w1 are constants.

Oxygen is placed into a closed system fitted with a piston capable of compressing the gas. The initial state is 100 L of O2 at 1.5 atm pressure and 400 K. The gas is compressed reversibly and isothermally until the pressure reaches 6.5 atm. Calculated the work done on the system.

The specific enthalpy of liquid n-hexane at 1 atm varies linearly with temperature and equals 25.8 kJ/kg at 30C and 129.8 kJ/kg at 50C.

Determine the equation that relates 𝑯 (kJ/kg) to T (C) and calculate the reference temperature on which the given enthalpies are based. Then derive an equation for 𝑼 (T) (kJ/kg) at 1 atm. (b) Calculate the average heat transfer rate required to cool 20.0 kg of liquid n-hexane from 80C to 20C in 5 min.

The specific enthalpy of liquid n-hexane at 1 atm varies linearly with temperature and equals 25.8 kJ/kg at 30C and 129.8 kJ/kg at 50C.

Determine the equation that relates 𝑯 (kJ/kg) to T (C) and calculate the reference temperature on which the given enthalpies are based. Then derive an equation for 𝑼 (T) (kJ/kg) at 1 atm. (b) Calculate the average heat transfer rate required to cool 20.0 kg of liquid n-hexane from 80C to 20C in 5 min.

A 1:2 mixture (by vol.) of CO and H2 is fed to a methanol converter. The conversion is 20percent complete. The products from the converter are sent to a separator where only 60percent of CH3OH (33.33 kmole MeOH/hr) is separated. The uncondensed CH3OH and unconverted gases are recycled and mixed with fresh feed.

For 100 kmoles/hr of fresh feed, Calculate (a) recycle rate and (b) recycle ratio (=recycle/feed).

Consider shooting a bullet of mass 𝑚 to three different big blocks. The resistance of the first block is assumed to be proportional to the bullet speed, that for the second block is proportional to 𝑣^(3/2), and that for the third block is proportional to 𝑣^2. If you fire at these blocks one by one with the same initial speed of 𝑣0 for your bullets, compute the farthest the bullet can travel in each of these all three cases. Note that the gravitational force for this problem is negligible.

Which dicarboxylic acid is expected to be least prone to forming a cyclic anhydride? Explain.

1. Succinic Acid COOH(CH3)2COOH

2. Glutaric Acid COOH(CH3)3COOH

3. Adipic Acid COOH(CH3)4COOH

Two aqueous sulfuric acid solutions containing 20.0 wt percent H2SO4 (SG = 1.139) and 60.0 wt percent H2SO4 (SG = 1.498) are mixed to form a 4.00 molar solution (SG = 1.213).

Q) Calculate the mass fraction of sulfuric acid in the product solution.

Find the general solution of the differential equation (regarding x as depending variable and y as independent). Primes denote derivatives with respect to x:

y' = (xy'+ y)y^3