A container is fitted with a movable piston of negligible mass and radius r = 0.061 m. Inside the container is liquid water in equilibrium with its vapor, as the drawing shows. The piston remains stationary with a 120-kg block on top of it. The air pressure acting on the top of the piston is one atmosphere. By using the vaporization curve for water in the figure below, find the temperature of the water.
To find the temperature of the water, we need to use the vaporization curve for water provided in the figure. However, the figure describing the vaporization curve is missing in the given question. Please provide the figure or the necessary information from the figure to proceed with the calculations.
To find the temperature of the water, we can use the relationship between pressure and temperature along the vaporization curve on the phase diagram.
Here are the steps to find the temperature:
1. Identify the given variables:
- Radius of the piston (r) = 0.061 m.
- Mass of the block on top of the piston (m) = 120 kg.
- Air pressure acting on the top of the piston (P) = 1 atmosphere.
2. Understand the setup:
- The system is in equilibrium, which means the pressure acting on the water surface must balance the weight of the block and the atmospheric pressure.
- The pressure exerted by the block is given by P_block = m * g / (π * r^2), where g is the acceleration due to gravity.
3. Calculate the pressure exerted by the block:
- Convert the atmospheric pressure to Pascals (Pa): 1 atmosphere = 101,325 Pa.
- Calculate P_block using the formula: P_block = m * g / (π * r^2).
- Remember to take the gravitational acceleration (g) as 9.8 m/s^2.
4. Determine the total pressure acting on the water:
- The total pressure acting on the water is the sum of the atmospheric pressure (P) and the pressure exerted by the block (P_block).
5. Use the vaporization curve on the phase diagram:
- Locate the point on the vaporization curve that corresponds to the total pressure found in step 4.
- Read the temperature value associated with that point on the curve.
By following these steps, you will be able to find the temperature of the water in the given container.
I do not have the figures in your book.
the vapor pressure of the water = 1 atm + 120 kg * 9.8 if Newtons are used/(piston area)