Calculate the Temperature and Pressure of a melting point

[romanski007]

Homework Statement

Ice is initially at -3C and 1atm. The pressure is increased adiabaticallu until the ice reaches the melting point. At waht temperature and pressure is this melting point? (Hint: At what point does a line whose slope is (dP/dT)_s cut a line whose slope is that of the fusion curve, -1.35 x 10^7 Pa / K?)

Relevant Equations

(dP/dT)_s = c_p / (Tv \beta) , c_p = 2.01 kJ / kg K, v = 1.09 x 10^-3 m^3 / kg and beta = 1.58 x 10^-4 / K

Adiabatic increase in pressure implies Tds=0, can someone tell me how to proceed?

 

[Chestermiller]

The problem statement gives you the equation for the derivative of P with respect to T at constant s, together with all the parameters you need to calculate it. You also have the equation for the slope of the fusion curve, and you know that, at 1 atm, the fusion curve passes through 0 C.

 

[romanski007]

The problem statement gives you the equation for the derivative of P with respect to T at constant s, together with all the parameters you need to calculate it. You also have the equation for the slope of the fusion curve, and you know that, at 1 atm, the fusion curve passes through 0 C.

The problem statement gives you the equation for the derivative of P with respect to T at constant s, together with all the parameters you need to calculate it. You also have the equation for the slope of the fusion curve, and you know that, at 1 atm, the fusion curve passes through 0 C.

Should I assume that the partial derivative of P wrt T remains constant throughout the process or that the specific volume of ice remains constant to work out the graph of P vs T for solid phase? Thanks.

 

[Chestermiller]

Should I assume that the partial derivative of P wrt T remains constant throughout the process or that the specific volume of ice remains constant to work out the graph of P vs T for solid phase? Thanks.

Assume constant partial derivative.