Answer:
1.737 kJ
Explanation:
Thinking process:
Step 1
Data:
Area of the shaft = 0.8 cm²
Combined mass of shaft and piston = (24.5 + 0.5) kg
= 25 kg
Piston diameter = 0.1 m
External atmospheric pressure = 1 bar = 101.3 kPa
Pressure inside the gas cylinder = 3 bar = 3 × 101.3 kPa
g = 9.81 m/s²
Step 2
Draw a free body diagram
Step 3: calculations
area of the piston = 0.0314 m²
Change in the elevation of the piston, [tex]\deltaz[/tex]
[tex]\delta[/tex]z = [tex]\frac{PE}{mg}[/tex]
= [tex]\frac{0.2*10x^{3} }{25*9.81}[/tex]
= 0.82 m
Next, we evaluate the work done by the shaft:
[tex]W_{s} = F_{s} Z[/tex]
= (1668) ( 0.082)
= 1. 37 kJ
Net area for work done = A (piston) - Area of shaft
= [tex]\pi*(0.1)^{2} - 0.8 cm^{2}[/tex]
= 77.7 cm²
= 0.007774 m²
Work done in overcoming atmospheric pressure:
Wₐ = PAZ
=101.3 kPa * 0.007774 * 0.82
= 0.637 kJ
total work = work done by shaft + work to overcome atmospheric pressure = 0.367 + 1.37
= 1.737 kJ Ans
In the process of analyzing a thermodynamic system it is important to identify what system is being worked on and the processes and properties if the system
The magnitude of the force acting on the shaft, is approximately 1,336.5 N
The reason the value for the force magnitude acting on the shaft is correct is as follows:
The known parameters are:
The cross-sectional area of the shaft, Aₐ = 0.8 cm²
The required gas pressure in the cylinder, P = 3 bar
The mass of the piston, m₁ = 24.5 kg
The mass of the shaft, m₂ = 0.5 kg
The diameter of the piston, D = 10 cm
The atmospheric pressure, Pₐ = 1 bar
Required:
The magnitude of the force F acting on the shaft
Solution:
The force due to the gas in the cylinder, [tex]\mathbf{F_{gas}}[/tex], is given as follows;
[tex]F_{gas}[/tex] = 3 bar × π × (10 cm)²/4 = 2,359.19449 N
The force due to the atmosphere, [tex]\mathbf{F_{atm}}[/tex], is given as follows;
[tex]F_{atm}[/tex] = 1 bar × ((π × (10 cm)²/4) - 0.8 cm²) ≈ 777.4 N
The force due to the piston and shaft, [tex]\mathbf{F_{ps}}[/tex], is given as follows;
[tex]F_{ps}[/tex] = (24.5 kg + 0.5 kg) × 9.81 m/s² = 245.25 N
The magnitude of the force acting on the shaft, F = [tex]F_{gas}[/tex] - ([tex]\mathbf{F_{atm}}[/tex] + [tex]\mathbf{F_{ps}}[/tex])
∴ F = 2,359.19449 N - (777.4 N + 245.25 N) ≈ 1,336.5449 N
The magnitude of the force acting on the shaft, F ≈ 1,336.5 N
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