Calculate the work done when a system raises a volume of water of radius 5.0mm through 10cm in thermodynamic.
To calculate the work done when a system raises a volume of water through a certain height, we need to know the force acting on the system and the displacement of the system.
In this case, the force acting on the system is the weight of the water. The weight can be calculated using the formula:
Weight = mass × acceleration due to gravity
The mass of the water can be calculated using its density and volume:
Mass = density × volume
The density of water is approximately 1000 kg/m³.
The volume of a cylinder can be calculated using the formula:
Volume = π × radius² × height
Let's plug in the given values:
Radius = 5.0 mm = 0.005 m
Height = 10 cm = 0.1 m
Now we can calculate the volume of water:
Volume = π × (0.005 m)² × 0.1 m
Volume ≈ 7.85 × 10⁻⁶ m³
Next, we can calculate the mass of the water:
Mass = 1000 kg/m³ × 7.85 × 10⁻⁶ m³
Mass ≈ 7.85 kg
Now, we can calculate the weight of the water using the relationship Weight = Mass × acceleration due to gravity:
Weight ≈ 7.85 kg × 9.8 m/s²
Weight ≈ 76.73 N
Finally, we can calculate the work done using the formula:
Work = Force × Displacement
In this case, the force acting on the system is the weight of the water, and the displacement is the height through which the water is raised. So:
Work = 76.73 N × 0.1 m
Work ≈ 7.67 J
Therefore, the work done when the system raises a volume of water of radius 5.0 mm through 10 cm is approximately 7.67 Joules.