Final answer:
To find the work required to pump the water out of the spout, we need to consider the change in pressure and volume of the water. The work required is 75.975 J.
Step-by-step explanation:
To find the work required to pump the water out of the spout, we need to consider the change in pressure and volume of the water.
First, let's calculate the change in pressure:
The initial pressure is given by the ambient pressure, which is 1.00 atm. The final pressure is 0, since the water flows out until the gauge pressure at the bottom of the dispenser is 0. The change in pressure is then 1.00 atm - 0 = 1.00 atm.
To calculate the volume of water that flows out, we can use the equation:
Volume = Area x Height
The area of the base of the dispenser is given by:
Area = length x width = 25 cm x 10 cm = 250 cm² = 0.025 m²
The change in height is 3.0 cm, or 0.030 m.
So, the volume of water that flows out is:
Volume = 0.025 m² x 0.030 m = 0.00075 m³
Finally, to find the work required to pump the water out, we can use the equation:
Work = Pressure x Volume
Work = 1.00 atm x 0.00075 m³ = 0.75 atm·m³
Since 1 atm·m³ = 101.3 J, the work required to pump the water out is:
Work = 0.75 atm·m³ x 101.3 J/atm·m³ = 75.975 J