Calculating Final Pressure for a Metal Undergoing Temperature and Volume Changes

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SUMMARY

The discussion focuses on calculating the final pressure of a metal subjected to temperature and volume changes. The metal has a volume expansivity of 5 x 10^-5 K^-1 and isothermal compressibility of 1.2 x 10^-11 Pa^-1, initially at a pressure of 1 x 10^5 Pa, a volume of 5 liters, and a temperature of 20 degrees Celsius. The process involves two stages: first, an isobaric temperature increase of 12 degrees Celsius, followed by isothermal compression to account for a volume increase of 0.5 cm^3. The final pressure is determined by applying the appropriate equations for each stage of the process.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically isobaric and isothermal processes.
  • Familiarity with the concepts of volume expansivity and isothermal compressibility.
  • Proficiency in using the equation Pf - Pi = B/K (Tf - Ti) for pressure calculations.
  • Basic knowledge of unit conversions, particularly between liters and cubic centimeters.
NEXT STEPS
  • Study the derivation and application of the ideal gas law in relation to pressure changes.
  • Explore advanced thermodynamic equations that incorporate both temperature and volume changes.
  • Learn about the implications of isothermal compressibility in real-world materials.
  • Investigate numerical methods for solving complex thermodynamic problems involving multiple variables.
USEFUL FOR

This discussion is beneficial for students and professionals in materials science, mechanical engineering, and thermodynamics, particularly those involved in pressure calculations and thermal analysis of metals.

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Moved from a technical forum, so homework template missing
A metal whose volume of expansivity is 5 x 10^‐5 K^‐1 and isothermal compressibility of 1.2x10^‐11 Pa^‐1 is at a pressure of 1 x10^5 Pa, volume of 5 litres and a temperature of 20 degrees Celsius undergoes a temperature rise of 12 degrees Celsius and an increase in volume of 0.5 cm^3. Calculate the final pressure.

So I feel like I should be using this equation: Pf - Pi = B/K (Tf-Ti) but I know that this formula assumes constant volume. I'm not sure how to incorporate the change in volume.
 
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Do it in two stages. Step 1, isobaric temperature increase of 12 K. What is the change in volume?
Step 2, isothermal compression to final volume. What is the change in volume in this step? So what is the change in pressure?
 

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