Answer:
Maximum shear stress is;
τ_max = 1427.12 psi
Explanation:
We are given;
Power = 2 HP = 2 × 746 Watts = 1492 W
Angular speed;ω = 450 rev/min = 450 × 2π/60 rad/s = 47.124 rad/s
Diameter;d = 1 in
We know that; power = shear stress × angular speed
So,
P = τω
τ = P/ω
τ = 1492/47.124
τ = 31.66 N.m
Converting this to lb.in, we have;
τ = 280.2146 lb.in
Maximum shear stress is given by the formula;
τ_max = (τ•d/2)/J
J is polar moment of inertia given by the formula; J = πd⁴/32
So,
τ_max = (τ•d/2)/(πd⁴/32)
This reduces to;
τ_max = (16τ)/(πd³)
Plugging in values;
τ_max = (16 × 280.2146)/((π×1³)
τ_max = 1427.12 psi
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Answer:
a)W=12.62 kJ/mol
b)W=12.59 kJ/mol
Explanation:
At T = 100 °C the second and third virial coefficients are
B = -242.5 cm^3 mol^-1
C = 25200 cm^6 mo1^-2
Now according isothermal work of one mole methyl gas is
W=-
a=
b=
from virial equation

And

a=
b=
Now calculate V1 and V2 at given condition

Substitute given values
= 1 x 10^5 , T = 373.15 and given values of coefficients we get

Solve for V1 by iterative or alternative cubic equation solver we get

Similarly solve for state 2 at P2 = 50 bar we get

Now

a=241.33
b=30780
After performing integration we get work done on the system is
W=12.62 kJ/mol
(b) for Z = 1 + B' P +C' P^2 = PV/RT by performing differential we get
dV=RT(-1/p^2+0+C')dP
Hence work done on the system is

a=
b=
by substituting given limit and P = 1 bar , P2 = 50 bar and T = 373 K we get work
W=12.59 kJ/mol
The work by differ between a and b because the conversion of constant of virial coefficients are valid only for infinite series
The change in annual cost when Q is increased from 340 to 341 is -1.23 and the instantaneous rate of change when Q = 340 is -1.25
<h3>How to find the Instantaneous rate of change?</h3>
The annual inventory cost C for a manufacturer is given as;
C = (1012000/Q) + 7.5Q
where Q is the order size when the inventory is replenished.
Now, the change in C can be calculated by evaluating the cost function at Q = 340 and Q = 341
Change in C = [1,012,000/341 + 7.5*341] - [1,012,000/340 + 7.5*340] ≈ -1.23
Instantaneous rate of change in C is first order derivative C':
C'(Q) = -1,012,000/(Q²) + 7.5
C'(340) = -1,012,000/(340²) + 7.5 ≈ -1.25
Read more about Instantaneous rate of change at; brainly.com/question/14666106
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