# Supercooled Steam Homework: Solving for Tf, Condensation Fraction & ΔS

• Ariel Jo
In summary: The conversation discusses the process of supercooling steam to 95˚C at 1 atm, causing it to partially condense into liquid water in a thermally-insulated vessel. The questions asked are: (a) when the system reaches equilibrium, what will the final temperature be? (b) what fraction of the water will condense? and (c) what is the change in entropy for this process? The ideal gas equation and the equation for change in entropy are mentioned as possible equations to use. The conversation also mentions the assumptions made for the volume and pressure in the calculations. The final temperature is found to be 100˚C, and the question is posed about the heat given off and the heat of vapor
Ariel Jo

## Homework Statement

You have 0.50 mol of steam which has been supercooled to 95˚C at 1 atm. Since the steam is below the boiling/condensation point, it proceeds to partially condense into liquid water. This happens in a thermally-insulated vessel at constant pressure.
(a) When the system re-attains equilibrium, what will the final temperature be?
(b) What fraction of the water will condense?
(c) Calculate ΔS for this process.

## Homework Equations

ideal gas equation (the gas is assumed to behave ideally)
deltaS=n*Cp*ln(Tf/Ti)

## The Attempt at a Solution

From PV=nRT, obtained an initial volume of steam of 15.1L but unsure how to proceed... Vf and Tf are both unknowns but should not be equal to Vi and Ti (from common sense - steam at 95degC will both condense and cool spontaneously.) Can easily find change in entropy from knowing final temperature... Would U=3/2RT be useful in this situation?

Last edited:
Some hints:

Lacking other data, assume the water condenses until it reaches equilibrium.

Since the pressure is held constant, assume the volume is variable.

This seems to give a final temperature of 100º C. (The boiling point of water.)

So the basic question seems to be, how much water has to condense to heat the vapor back to 100º C.?

q(gained by water)=q(lost by steam), and at constant pressure this would be q=n*Cp*deltaT for both substances. Setting them equal to each other would give moles of each, but there are no calculations to get 100degC as the equilibrium temp, just the (seemingly sound, but I'm not a physics specialist) logic that for steam to not be supercooled it must be at 100degC or higher (when the pressure is a constant 1atm), if I understand you correctly.
Thanks for the help!

How much heat is given off (per mole) when steam condenses to liquid water at a constant temperature of 100 C? What is the heat of vaporization of water at 100 C?

Chet

Ariel Jo

## 1. What is supercooled steam?

Supercooled steam is steam that has been cooled below its normal boiling point without undergoing a phase change into liquid water.

## 2. Why is solving for Tf, condensation fraction, and ΔS important in supercooled steam homework?

Solving for Tf (final temperature), condensation fraction, and ΔS (change in entropy) is important in supercooled steam homework because it helps us understand the behavior and properties of steam at temperatures below its boiling point. It also allows us to calculate the amount of condensation that will occur and the change in entropy, which are important factors in many industrial processes involving steam.

## 3. How do you solve for Tf in supercooled steam homework?

Tf can be solved for using the Clausius-Clapeyron equation, which relates the change in temperature to the change in pressure in a phase transition. In supercooled steam, the pressure remains constant, so the equation simplifies to Tf = Tb + (ΔHvap/R) * ln(P/Pb), where Tb is the normal boiling point, ΔHvap is the enthalpy of vaporization, R is the gas constant, P is the pressure, and Pb is the normal boiling point pressure.

## 4. What is the condensation fraction in supercooled steam?

The condensation fraction in supercooled steam is the ratio of the amount of steam that has condensed into liquid water to the total amount of steam present. It is represented by the symbol ξ and can be calculated using the equation ξ = (P/Psat)^((ΔHvap/R)/T), where Psat is the saturation pressure at the final temperature Tf.

## 5. How does ΔS relate to supercooled steam?

ΔS, or the change in entropy, is important in supercooled steam as it indicates the amount of disorder or randomness in the system. In the case of supercooled steam, ΔS can be calculated using the equation ΔS = (ΔHvap/Tf) - R * ln(P/Pb), where ΔHvap is the enthalpy of vaporization, Tf is the final temperature, P is the pressure, and Pb is the normal boiling point pressure. ΔS will be negative for supercooled steam, indicating a decrease in disorder as the steam condenses into liquid water.