Answer:
(a) 151.84 kJ
(b) 2.922 kJ/K
Explanation:
(a) The parameters given are;
Mass of hydrogen gas, H₂ = 0.1 kg = 100 g
Molar mass of H₂ = 2.016 g/mol
Number of moles of H₂ = 100/2.016 = 49.6 moles
V₁ = mRT/P = 0.1×4.12×300/1000 = 0.1236 m³
P₁/P₂ = (V₂/V₁)^k
V₂ = (P₁/P₂)^(1/k)×V₁ =0.1236 × (1000/500)^(1/1.4) = 0.3262 m³
Boundary work done = (V₂ - V₁)(P₂ + P₁)/2 = (0.3262 - 0.1236)*(500 + 1000)/2 = 151.84 kJ
(b) Entropy generated ΔS = Cv · ㏑(T₂/T₁) + R ·㏑(v₂/v₁)
=10.18 × ㏑(270/300) + 4.12 ·㏑(0.3262/0.1236) = 2.922 kJ/K.
Determine size of a standard square key made of 1045 hot rolled steel for a 2 inch DIA shaft transmitting 100 HP at 500 rpm with factor of safety 2.5 for yield in direct shear. W____inch L_____inch
Answer:
Width = Length = 1.148 inches
Explanation:
We have been given the following data:
D = diameter = 2 inch = 0.0508m
P = Power = 100 HP = 74570 W
N = 500 rpm
Safety Factor = 2.5
Step 1:
We need to find yield strength which is represented by σ(y).
σ(y) for 1045 hot rolled steel = 330MPa
Step 2:Find Shear Strength. Formula is given:
τ(y) = σ(y) / 2
τ(y) = 330 / 2
τ(y) = 165 MPa
τ(y) = 165 × 10⁶ Pa
τ(y) = 165 × 10⁶ kg.m⁻¹.s⁻²
Step 3:
Find Torque. Formula is given:
T = 60P / 2πN
T= (60)(74570) / 2π(500)
T = 1424.9 Nm
Step 4:Find Shear Force. Formula is given:
F = 2T/d
F = 2(1424.9)/0.0508
F = 56098.43 N
F = 56098.43 kg.m.s⁻²
Step 5:Find length by the given formula:
F/L² = τ(y)/Safety factor
Rearrange for L:
L = √(F· Safety factor / τ(y))
Substitute the values found in previous steps to calculate L.
L = 0.02915 meters
Convert it into inches:
L = 1.148 in
As it si a square key:
L = W
Width = 1.148 in