Calculating Final Pressure in Isochoric Thermo Process

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SUMMARY

The discussion focuses on calculating the final pressure in an isochoric thermodynamic process using the relationship between temperature change and pressure change. The key equation derived is ΔP = βKΔT, where β represents expansivity, K is the isothermal bulk modulus, and ΔT is the change in temperature. The user initially struggled with the integral leading to an incorrect conclusion that final pressure equals initial pressure. The correct approach involves recognizing the relationship between the variables in the context of constant volume.

PREREQUISITES
  • Understanding of isochoric processes in thermodynamics
  • Familiarity with the concepts of thermal expansivity (β) and isothermal bulk modulus (K)
  • Basic knowledge of calculus, particularly integration
  • Ability to manipulate thermodynamic equations
NEXT STEPS
  • Study the derivation of the ideal gas law under isochoric conditions
  • Learn about the implications of thermal expansivity in different materials
  • Explore the application of the isothermal bulk modulus in real-world scenarios
  • Investigate advanced thermodynamic equations and their applications in engineering
USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, mechanical engineers, and anyone involved in calculating pressure changes in closed systems during thermal processes.

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I'm trying to calculate the final pressure. I was given initial and final temperatures as well as initial pressure, expansitivy and isothermal bulk modulus. I was also told the volume is constant.

Since volume is constant I figured dV=0

so in the formula dV=VβdT - VKdP it reduces to:

βdT=KdP

I know that I need to solve for dP but I think I'm doing something wrong in my integral because I end up with the final pressure being the same as the initial pressure which I know is wrong. How do I solve that equation for dP?
 
Science news on Phys.org
The equation should be $$dV=V\beta dT-V\frac{dp}{K}$$ So, $$\Delta P=\beta K \Delta T$$
 

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