Thermal physics- Can you make good tea at a certain pressure!?

H.fulls

1. The problem statement, all variables and given/known data
According to experts good tea can only be made at temperatures greater than 97 degrees celsius. If this is true, can you brew good tea at elevation 4km (Pressure = 6.2*[itex]10^{4}[/itex]Pa) . Given that latent heat of vaporisation for water is 2.4*[itex]10^{6}[/itex] J/kg and water has a molar mass of 18g.


2. Relevant equations
Clausius-clapeyron equation [itex]\frac{dp}{dT}[/itex] = [itex]\frac{L}{T(V2-V1)}[/itex]
but V1 is negligable so [itex]\frac{dp}{dT}[/itex] = [itex]\frac{L}{TV2}[/itex]

Ideal gas equation pV=nRT


3. The attempt at a solution

Tried to integrate so have [itex]\int\frac{1}{p}dp[/itex]=[itex]\frac{L}{R}[/itex][itex]\int\frac{1}{T^{2}}dT[/itex]
from substituting in V = [itex]\frac{RT}{p}[/itex] from ideal gas equation.
But dont really know what to do from here! I dont know what limits to put in for the integral or if im just going about this all wrong from the start!
Ive been told the clausius-clapeyron statement must be used by my professor!
Any suggestions would be helpful! Thankyou!

JesseC

I think what the question is really asking is, at what temperature does water boil at an altitude of 4km? If it boils at over 97C then the tea you make will be 'good', if not, it will be 'bad'.

Why don't you try integrating from p0 to p1 and from T0 to T1 where p0 and T0 are reference pressure and temperatures which you know. The question then becomes, what is the pressure at 4km above sea level?

haruspex

The pressure at 4km was given.

rude man

Boiling is when saturated vapor pressure = atmospheric pressure. So get a table of sat. vapor pressure vs. temperature for water and see if T corresponding to your altitude pressure is > 97C.

JesseC

The question specifically requires use of the Clausius-clapeyron equation. The answer can be reached using the equation, a couple of lines of algebra and substitution of the correct values. Tables really aren't needed :/