Calculate the Temperature and Pressure of a melting point

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Homework Help Overview

The discussion revolves around calculating the temperature and pressure at the melting point of a substance, focusing on the relationship between pressure and temperature during phase changes, particularly in the context of the fusion curve.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the implications of adiabatic processes and the equations provided in the problem statement, including the derivative of pressure with respect to temperature at constant entropy. There are questions about the assumptions regarding the constancy of the partial derivative and specific volume of ice in relation to the pressure-temperature graph for the solid phase.

Discussion Status

Some participants have reiterated the information given in the problem statement, while others are exploring assumptions that could affect the analysis. There is an ongoing examination of how to approach the relationship between pressure and temperature, with no clear consensus yet on the assumptions to adopt.

Contextual Notes

The problem statement provides specific equations and parameters necessary for the calculations, and there is a mention of the fusion curve passing through 0°C at 1 atm, which may influence the assumptions being discussed.

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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