As a result of a chemical spill, benzene is evaporating at the rate of 1 gram per minute into a room that is 6 m * 6 m * 3 m in size and has a ventilation of 10 m3/min.
a- Compute the steady state concentration of benzene in the room.
b- Assuming the air in the room is initially free of benzene, compute the time necessary for benzene to reach 95 percent of the steady-state concentration.

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The 5-page solution shows how to construct and solve the differential equation that models the situation.

Consider the following system in Fig.2 (see attached file). Determine the steadystate error for unit ramp input. What will be the effect of B and K on steady-state error?

A countries production function is Y=5K^.5 L^.5
Assume that the rate of depreciation as well as the rate of saving are each .10. Also assume that there is no technological nor population growth.
A. What is the steadystate level of capital per worker?
B. What is the steadystate level of output per worker?
C. Suppose that t

A stable and highly soluble pollutant is dumped into a lake at the rate
of 0.19 tonnes per day. The lake volume is 2E7 m3 and
the average water flow-through rate is 8E4 m3 per day. Ignore evaporation
from the lake surface and assume the pollutant is uniformly mixed in the lake.
What eventual steady-state concentration will t

Just before the switch is opened at t=0, the current through the inductor is 1.70 mA in the direction shown in figure (PLEASE SEE ATTACHMENT). Did steady-state conditions exist just before the switch was opened?
L = 0.9 mH;
R1 = 6k Ohm;
R2 = 6k Ohm;
R3 = 3k Ohm;
Vs = 12V

Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
(a) 10y' = 5y and y(0) = 1. The answer is y(t) = e^(1/2t), but having trouble arriving at that answer
(b) 4y' - 4y = -8 and y(0) = 10. The answer

For the circuit in attached image,
a) Find the Laplace voltage Vout(s).
b) Find the inverse Laplace Transform of the voltage.
c) Find the steady-state voltage.
Please show full work with explanations.

Problem 1:
Consider the closed-loop transfer function
T(s) = 10K/(s2 + 20s + K)
1. Obtain the family of step responses for K=10, 100, and 500. Co-plot the responses and develop a table that includes the following:
a. Percent overshoot
b. Settling time
c. Steady-state error.
Figure 1
Problem 2:
A negat

Consider a stoppered flask containing benzene, iodine, and air, which has reached equilibrium at 298K. Which one of the following statements concerning the system at equilibrium is true?
(a) The pressure of the vapour phase is not constant.
(b) Evaporation of the liquid continues.
(c) The colour of the liquid phase will

1. A production process contains a machine that deteriorates rapidly in both quantity and output under heavy usage, so it is inspected at the end of each day. Immediately after inspection the condition of the machine is noted and classified into one of four possible states:
State
0: good as new
1: Operable - minimum deteri