The normal melting point of H2O is 273.15 K, and deltaH fusion is 6010 J/mol. Calculate the change in the normal melting point at 175 and 625 bar assuming that the density of the liquid and solid phases remains constant at 997 and 917 kg/m^3 respectively. Explain the sign of your answer.
So I had no problem calculating:
when P= 175 bar, deltaT= -1.25 K
when P= 625 bar, deltaT= -4.48 K
Assuming my answers are correct, can someone explain the negative signs in the context of the question?
I think the negative sign simply means that at increased pressure the melting point decreases by 1.25 and 4.48 K respectively but I don't know if this is sufficient explanation or not.
I think the negative sign implies that the slope between S and L is negative so as you increase Pressure you will get a small T. But what formula did you use to find delta T.
I went
(dP/dT)fusion=deltaSm(fusion)/deltaVm(fusion)
=deltaHm(fusion)/Tfusionm(1/pliq. - 1/psolid)
=-140 barK^-1
So then deltaT=-deltaP/140
What is L? volume (litres?)
I think Joe is referring to the phase diagram and the slope of the S(solid)/L(liquid) line which is negative.
Yeah I'm referring to the phase diagram and the Solid/Liquid line
The negative signs in the context of the question indicate a decrease in the normal melting point of water with increasing pressure. To understand why this is the case, let's consider the phase diagram of water.
The phase diagram of a substance shows its different phases (solid, liquid, and gas) as a function of temperature and pressure. In the case of water, the phase diagram typically shows a negative slope for the melting curve (the line separating the solid and liquid phases) at relatively low pressures.
Under normal conditions (i.e., at atmospheric pressure), the normal melting point of water is 273.15 K. This means that at this temperature, water undergoes a phase transition from a solid to a liquid. However, when pressure is applied to the system, the melting point of water decreases. This is due to the fact that applying pressure compresses the water molecules and makes it more difficult for them to arrange into a solid lattice structure.
Now, let's consider the specific calculations you provided. For P = 175 bar, the change in the normal melting point is -1.25 K. This means that the melting point of water decreases by 1.25 K when the pressure is increased to 175 bar. Similarly, for P = 625 bar, the change is -4.48 K, indicating a larger decrease in the melting point compared to 175 bar.
In summary, the negative signs indicate a decrease in the normal melting point of water with increasing pressure. This behavior is characteristic of many substances and is attributed to the compression of the molecules under pressure.