Q66PE - College Physics (Urone)

Question

Question: (a) At what depth in freshwater is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth?

Step-by-Step Solution

Answer

Answer

1. the depth of water is calculated as 22.469 m. 
2. The boiling point of water is 374.3°C. 
3. Temperature increases with altitude due to high pressure.

Step 1: Describe the scenario

Here, the surface is at sea level. So, the critical pressure has a contribution from the pressure of air and the pressure of water. The critical pressure of water is the pressure at its critical point. Its value is 22.12 x 10⁶ Pa. To calculate the depth, first, we need to calculate the pressure of the water.

Step 2: Solution of part (a)

The pressure of air is the atmospheric pressure. Its value is 1.013×10⁵ Pa. So, we know the pressure of air and the critical pressure. The pressure of water can be calculated by subtracting the pressure of air from the critical pressure.

$$\begin{gathered} \text{essure of water}=Critical\text{ Pressure}-\text{Pressure of air} \\ =22.12\times {10}^6 Pa-1.013\times {10}^5 Pa \\ =22.02\times {10}^6 Pa \end{gathered}$$

Therefore, the pressure of water is 22.02×10⁶ Pa. The pressure of water and its depth are related as follows;

$$\begin{gathered} P=h\rho g \\ h=\frac{P}{\rho g} \end{gathered}$$

Here is the pressure, the density, and the acceleration due to gravity. The density of water is 1000 Kg/m³, and the acceleration due to gravity is 9.8 m/s². Substitute these values and calculate the depth.

$$\begin{gathered} h=\frac{22.02\times {10}^{6}Pa}{1000 kg/m^3\times 9.8 m/s^2} \\ =22.469 m \end{gathered}$$

Therefore, the depth of water is 22.469 m.

Step 2: Solution of part (b)

The boiling point is the temperature at which vapor pressure becomes equal to atmospheric pressure. Since the vapor pressure of water and the critical are almost equal, the temperature that corresponds to the critical pressure is the boiling point. That means the boiling point is equal to the critical temperature. So, the boiling point is 374.3°C.

Step 3: Solution of part (c)

A high temperature is required to boil water at a high depth because pressure increases with depth. The boiling point is the temperature at which the vapor pressure and the surrounding pressure become equal. The temperature rises in direct proportion to the pressure. So, at a higher depth, the temperature will be higher.

Thus, the depth of water is calculated as 22.469 m. The boiling point of water is 374.3°C. Temperature increase with altitude due to high pressure.