Answer:
The long derivation for work of a mechanically reversible, isothermal compression was done with detailed steps as shown in the attachment.
Explanation:
what is applied here is a long derivation from Work done in an isobaric process, the expression for the compressibility factor (Z) and the equation of state that was given. The requisite knowledge of Differentiation and Integration was used.
The detailed derivation from firs principle is as shown in the attachment.
Answer:
Magnitude of force P = 25715.1517 N
Explanation:
Given - The wires each have a diameter of 12 mm, length of 0.6 m, and are made from 304 stainless steel.
To find - Determine the magnitude of force P so that the rigid beam tilts 0.015∘.
Proof -
Given that,
Diameter = 12 mm = 0.012 m
Length = 0.6 m
= 0.015°
Youngs modulus of elasticity of 34 stainless steel is 193 GPa
Now,
By applying the conditions of equilibrium, we have
∑fₓ = 0, ∑ = 0, ∑M = 0
If ∑ = 0
⇒×0.9 - P × 0.6 = 0
⇒×3 - P × 2 = 0
⇒ =
If ∑ = 0
⇒×0.9 = P × 0.3
⇒ ×3 = P
⇒ =
Now,
Area, A = = 1.3097 × 10⁻⁴ m²
We know that,
Change in Length , =
Now,
= 9.1626 × 10⁻⁹ P
= 1.83253 × 10⁻⁸ P
Given that,
= 0.015°
⇒ = 2.618 × 10⁻⁴ rad
So,
⇒2.618 × 10⁻⁴ = ( 1.83253 × 10⁻⁸ P - 9.1626 × 10⁻⁹ P) / 0.9
⇒P = 25715.1517 N
∴ we get
Magnitude of force P = 25715.1517 N