# Reduce Melting Temp. by applying Pressure

1. Jun 3, 2012

### Ryomega

1. The problem statement, all variables and given/known data

The molar volume of ice at 273.15K and 101.33 kPa is V1=19.6 cm3
That of water V2=18.00 cm3.
Latent heat of melting of ice is L=6.0 kJ mol-1.

Find the pressure that must be applied to reduce the melting point by 1 K.

2. Relevant equations

Clausius-Clapeyron

$\frac{dP}{dT}$ = $\frac{L}{TΔV}$

ΔV = (V2-V1)

3. The attempt at a solution

The problem I am having is fundamental, this is not the usual find vapour pressure question, which is what caught me off guard. So what I'm asking is a way to set this question up. This is where I've gotten so far.

$\frac{dP}{dT}$ = $\frac{L}{TΔV}$

dP = $\frac{L}{TΔV}$ dT

P = $\frac{L log (T)}{ΔV}$

L log (T) = PΔV

Log (T) = $\frac{PΔV}{L}$

T = exp [$\frac{PΔV}{L}$]

Do I subtract 1 from T and solve for P? It doesn't feel right. Or did I completely mess it up?
If so please show me the set up, I should be ok with the rest.

2. Jun 3, 2012

### rude man

dp = (L/Δv)dT/T

then how about computing the definite integral instead of the indefinite one?

Δp = ?

3. Jun 3, 2012

### Ryomega

*Face Palm* Set limit from (T) to (T-1) I take it. Thanks

4. Jun 3, 2012

### rude man

Right. And use the appropriate value of T of course.

5. Jun 3, 2012

### Ryomega

Yup yup! Thanks! I feel a tad retarded for not seeing that.

6. Jun 3, 2012

### rude man

Don't. It's always a bit rough the first time you run into a new topic ...