Answer:
x(t) = −39e
−0.03t + 40.
Explanation:
Let V (t) be the volume of solution (water and
nitric acid) measured in liters after t minutes. Let x(t) be the volume of nitric acid
measured in liters after t minutes, and let c(t) be the concentration (by volume) of
nitric acid in solution after t minutes.
The volume of solution V (t) doesn’t change over time since the inflow and outflow
of solution is equal. Thus V = 200 L. The concentration of nitric acid c(t) is
c(t) = x(t)
V (t)
=
x(t)
200
.
We model this problem as
dx
dt = I(t) − O(t),
where I(t) is the input rate of nitric acid and O(t) is the output rate of nitric acid,
both measured in liters of nitric acid per minute. The input rate is
I(t) = 6 Lsol.
1 min
·
20 Lnit.
100 Lsol.
=
120 Lnit.
100 min
= 1.2 Lnit./min.
The output rate is
O(t) = (6 Lsol./min)c(t) = 6 Lsol.
1 min
·
x(t) Lnit.
200 Lsol.
=
3x(t) Lnit.
100 min
= 0.03 x(t) Lnit./min.
The equation is then
dx
dt = 1.2 − 0.03x,
or
dx
dt + 0.03x = 1.2, (1)
which is a linear equation. The initial condition condition is found in the following
way:
c(0) = 0.5% = 5 Lnit.
1000 Lsol.
=
x(0) Lnit.
200 Lsol.
.
Thus x(0) = 1.
In Eq. (1) we let P(t) = 0.03 and Q(t) = 1.2. The integrating factor for Eq. (1) is
µ(t) = exp Z
P(t) dt
= exp
0.03 Z
dt
= e
0.03t
.
The solution is
x(t) = 1
µ(t)
Z
µ(t)Q(t) dt + C
= Ce−0.03t + 1.2e
−0.03t
Z
e
0.03t
dt
= Ce−0.03t +
1.2
0.03
e
−0.03t
e
0.03t
= Ce−0.03t +
1.2
0.03
= Ce−0.03t + 40.
The constant is found using x(t) = 1:
x(0) = Ce−0.03(0) + 40 = C + 40 = 1.
Thus C = −39, and the solution is
x(t) = −39e
−0.03t + 40.
The heat (Q) required to raise the temp of a substance is:<span>Q=m∗Cp∗ΔT</span><span> where m is the mass of the object (25.0g in this case), Cp is the specific heat capacity of the substance (for water Cp = 1.00cal/gC, or 4.18J/gC,
and Dt is the change in temp.
You'll have to solve this twice, once with the Cp in calories, and once with the Cp in joules.
</span><span>1380.72 Joules</span>
Kijoknm
gg hv jnb vcxbnbvcvbnmnbvmnb
Answer:
The radial velocity curve describes how fast a star is moving in its orbit around a center of mass ( m )
Curve amplitude : This is the maximum value of the radial velocity curve
Radial velocity shape ; The shape of Radial velocity curve is parabolic in nature
Orbital period : Orbital period is the time taken by the star to make one complete rotation in its orbit
Explanation:
The radial velocity curve describes how fast a star is moving in its orbit around a center of mass ( m ) while Curve amplitude is the maximum value of the radial velocity curve also The shape of Radial velocity curve is parabolic in nature. and Orbital period is the time taken by the star to make one complete rotation in its orbit
equal to 1
Explanation:
All conversion factors used in any calculation is usually a ratio that is equal to 1. This is because when 1 is used to multiply or divide any number, the number stays the same.
- Conversion factors are useful in making the simplification of an expression very simple. They are usually ratios of 1.
- It follows that a conversion factor is a number that when multiplied or divided by itself will stay the same.
Learn more:
conversion factor: brainly.com/question/555814
#learnwithBrainly
