Calculate the Temperature and Pressure of a melting point

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SUMMARY

The discussion focuses on calculating the temperature and pressure of a melting point using thermodynamic principles. Participants emphasize the importance of the derivative of pressure (P) with respect to temperature (T) at constant entropy (s) and the slope of the fusion curve, particularly noting that at 1 atm, the fusion curve intersects at 0°C. The consensus is to assume that the partial derivative of P with respect to T remains constant throughout the process to accurately plot the graph of P versus T for the solid phase.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically adiabatic processes.
  • Familiarity with the concept of derivatives in the context of pressure and temperature.
  • Knowledge of the fusion curve and its significance in phase transitions.
  • Basic grasp of entropy and its role in thermodynamic equations.
NEXT STEPS
  • Study the derivation of the Clausius-Clapeyron equation for phase transitions.
  • Learn about the properties of ice and water under varying pressure and temperature conditions.
  • Research the implications of constant entropy in thermodynamic processes.
  • Explore graphical representations of phase diagrams, particularly for water and ice.
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, particularly those studying phase transitions, as well as researchers and engineers working with materials that undergo melting and solidification processes.

romanski007
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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?
 
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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.
 
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Chestermiller said:
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.
Chestermiller said:
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.
 
romanski007 said:
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.
 
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