Thermodynamics Homework: Entropy Change, Phase Equilibrium & More

[senan]

Homework Statement

(1a) What are the total change in energy and entropy if 250 g of water at 20◦C is heated
and vaporised to yield 250 g of steam, all at atmospheric pressure?

(1b) Find the change in the entropy of 250 g of liquid water at its boiling point when it is
vaporised at a pressure of 8 atm. Give a brief physical explanation for how this entropy
change compares with the entropy change for vaporisation at 1 atm pressure.

(1c) We can allow for a possible transition between two phases of a substance by adding
the term +μdN in the fundamental thermodynamic relation for dE. Derive the condition
for equilibrium between two phases at a fixed temperature and pressure.

Homework Equations

The Attempt at a Solution

1(a) S₂-S₁ = mC Integral form T1 to T2 of (dT/T) + Latent heat of transformation/373.15K

The latent heat wasn't given in the question so I'm wondering how to get around using it

1(b)

i was thinking of using S₂-S₁ = (1/T) integral from 1 to 2 of PdV but i can't figure how to eliminate the volume

1(c)
i don't have anything for this

 

[Astronuc]

Homework Statement

(1a) What are the total change in energy and entropy if 250 g of water at 20◦C is heated
and vaporised to yield 250 g of steam, all at atmospheric pressure?

(1b) Find the change in the entropy of 250 g of liquid water at its boiling point when it is
vaporised at a pressure of 8 atm. Give a brief physical explanation for how this entropy
change compares with the entropy change for vaporisation at 1 atm pressure.

(1c) We can allow for a possible transition between two phases of a substance by adding
the term +μdN in the fundamental thermodynamic relation for dE. Derive the condition
for equilibrium between two phases at a fixed temperature and pressure.

Homework Equations

The Attempt at a Solution

1(a) S₂-S₁ = mC Integral form T1 to T2 of (dT/T) + Latent heat of transformation/373.15K

The latent heat wasn't given in the question so I'm wondering how to get around using it

1(b)

i was thinking of using S₂-S₁ = (1/T) integral from 1 to 2 of PdV but i can't figure how to eliminate the volume

1(c)
i don't have anything for this

Is one familiar with steam tables in which properties such as specific enthalpy and specfic entropy are given as functions of pressure and temperature?

For water properties at 1 atm (1 bar) please see -
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html#c1


In part a, the liquid is subcooled with respect to saturation conditions. The liquid must be increased from 20°C to 100°C, and then the liquid changes phase to vapor at constant pressure.

 

[Mapes]

Welcome to PF, senan!

1(a). You're going to have to look up the enthalpy of vaporization (along with the heat capacity).

1(b). How about using the same equation as in 1(a), adjusted to the new conditions?

1(c). The fundamental statement of equilibrium is $dS=0$. Try to get there. Note that you'll have a $\mu\,dN$ term for each phase, with $dN_1=-dN_2$ (because any matter that leaves one phase joins the other).