Trouble Solving Volume of Condensed Water

In summary, the volume of condensed water is the amount of water that has been converted from its gaseous state to its liquid state due to changes in temperature and pressure. It can be calculated using the ideal gas law or by measuring the amount of water collected. The factors that affect the volume include temperature, pressure, and water vapor levels. Understanding the volume of condensed water is important in various fields and there are methods for controlling it, such as adjusting temperature and pressure, using dehumidifiers, and improving ventilation.
  • #1
kapatter
2
0
I'm having some trouble getting started on this one:

3.00×10^4 cm^3 of 300 degrees C steam at a pressure of 10.0 atm is cooled until it condenses. What is the volume of the liquid water? Give your answer in cm^3.

I figure you use pV=nRT to solve. I've been trying to rearrange it, but am confused. Any help would be greatly appreciated. Thanks.
 
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  • #2
Firstly, why is this is Quantum Physics?

Secondly, why don't you show us the equation that you get when you rearrange it?
 
  • #3


I understand your struggle with solving the volume of condensed water in this scenario. Let me provide some guidance to help you get started.

First, it is important to note that the ideal gas law, pV = nRT, cannot be directly applied in this situation as the steam is not an ideal gas. Instead, we will need to use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature and enthalpy of vaporization.

To begin, we can rearrange the equation to solve for the enthalpy of vaporization (ΔHvap):

ΔHvap = (RTln(P2/P1)) / (1/T2 - 1/T1)

Where P1 and T1 are the initial pressure and temperature of the steam, and P2 and T2 are the final pressure and temperature at which the steam condenses. In this case, P1 = 10.0 atm, T1 = 300 degrees C, and T2 = 100 degrees C (the boiling point of water).

Next, we can calculate the number of moles of water vapor using the ideal gas law:

n = PV/RT

Where V is the initial volume of the steam, which is given as 3.00×10^4 cm^3.

Once we have calculated the enthalpy of vaporization and the number of moles of water vapor, we can use the definition of enthalpy of vaporization (ΔHvap = Q/m) to calculate the amount of heat released when the steam condenses. This heat will be transferred to the surroundings and will cause the steam to condense into liquid water.

Finally, we can use the relationship between heat (Q), mass (m), and density (ρ) to calculate the volume of the liquid water:

V = m/ρ = Q/ρΔHvap

Where ρ is the density of water and can be found in a table or online.

I hope this helps you get started on solving the volume of condensed water in this scenario. Remember to carefully consider the units and conversions throughout the calculations. Good luck!
 

Related to Trouble Solving Volume of Condensed Water

1. What is the volume of condensed water?

The volume of condensed water refers to the amount of water that has been converted from its gaseous state to its liquid state due to a decrease in temperature or an increase in pressure. It is typically measured in units of volume, such as liters or cubic meters.

2. How is the volume of condensed water calculated?

The volume of condensed water can be calculated using the ideal gas law, which states that the volume of a gas is directly proportional to its temperature and inversely proportional to its pressure. Additionally, the volume can also be calculated by measuring the amount of water collected in a container after condensation occurs.

3. What factors affect the volume of condensed water?

The volume of condensed water is primarily affected by temperature, pressure, and the amount of water vapor present in the air. Higher temperatures and lower pressures will result in a larger volume of condensed water, while lower temperatures and higher pressures will result in a smaller volume.

4. Why is the volume of condensed water important to understand?

The volume of condensed water is important to understand in various fields such as meteorology, engineering, and environmental science. It can impact weather patterns, building insulation, and air quality, among other things. Additionally, understanding the volume of condensed water can also help in predicting and mitigating potential water damage.

5. What are some methods for controlling the volume of condensed water?

There are several methods for controlling the volume of condensed water, including adjusting the temperature and pressure, using dehumidifiers, and implementing proper ventilation systems. Additionally, sealing air leaks and insulating surfaces can also help reduce the amount of water vapor in the air and prevent condensation from occurring.

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