Engineering Answers

Derive and explain gauss’ law

When a pendulum of length 10 cm has swung so that 𝜃 is the radian measure of the angle formed by the pendulum and a vertical line, then if ℎ(𝜃) cm is the vertical height of the end of the pendulum above its lowest position, ℎ(𝜃) = 20 𝑠𝑖𝑛^2 𝜃/2 . Find the instantaneous rate of change of ℎ(𝜃) with respect to 𝜃 when (a) 𝜃 = 𝜋/3 and (b) 𝜃 = 𝜋/2

A pressure cooker has 1.0 kg of steam 0.8 dry at 3.0 bar. What amount of heat needs to be supplied

to raise its pressure to 4.0 bar?

Solve by using gaussian elimination

x+2y-3z=-1

-3x+y-2z=-7

5x+3y-4z=2

Find the equation of the hyperbola with center (4, - 1), transverse axis parallel to the Y-axis, distance between foci 10, latus rectum 9/2.

A study of the compressibility charts, Items B 19 through B 21, will reveal that certain combinations of PR and TR will produce compressibility factors of Z = 1, as if the gas were ideal. (a) List several of these combinations from Item B 20. (b) What will be the state (p psia, t°F) of a given fluid (other than ideal) to produce Z = 1 if that fluid is air? Ammonia? Helium?

A booster station compresses 50 kg/sec of methane from 14 atm, 285 K to 92 atm in a reversible and isothermal steady state steady-flow manner. Use the general ized fugacity coefficient chart (Item B 37) and calculate the compression work and the heat transfer. Now solve using ideal gas theory and compare answers.

The inreversible isomerization

A->B was carried out in a batch reactor and the following concentration-time data were obtained: T(min) 0 3 5 8 10 12 15 17.5

CA(mol/dm3) 4.0 2.89 2.25 1.45 1.0 0.65 0.25 0.07

(a) Use regression to determine the reaction order, a, and the specific reaction rate, ka.

The flat base of the bottom of an electric water heater is made of a 2 mm thick steel plate. thermal conductivity of 40 W/(m. oC), and an insulating plate with a thickness of 4 mm and thermal conductivity of 0.06 W/(m.oC). Between the steel and insulating plates there is an electrical resistance (RE) that dissipates a power of 800 W. 

Consider the steady state situation with boiling water at a temperature of 100 oC and with a coefficient of heat transfer by convection of 3000 W/(m2. oC), while the ambient air, which is in contact with the insulator, it remains at a temperature of 25oC and a convection heat transfer coefficient of 10 W/(m2.oC).

Considering a perfect thermal contact between the electrical resistance and the steel and insulating sheets and that the base of the heater has an area of 0.018 m2, determine: 

a) The temperature (TR) of the electrical resistance

b) The rate of heat lost to the air through of the insulating plate

ç). The rate of heat lost to water through the steel plate

piston-cylinder contains gas initially at 3500 kPaa with a volume of 0.03 mº. The gas is compressed during a process where pV 1.25 C to a pressure of 8500 kPaa. The heat transfer from the gas is 2.5 kJ. Determine the change in internal energy, neglecting changes in kinetic and potential energies.