Calculating Final Pressure in Isochoric Thermo Process

AI Thread Summary
To calculate the final pressure under constant volume conditions, the relationship between temperature change and pressure change is established using the formula βdT = KdP. The user correctly identifies that with constant volume, dV equals zero, simplifying the equation. However, confusion arises when integrating, leading to the incorrect conclusion that final pressure equals initial pressure. The correct approach involves recognizing that the change in pressure, ΔP, can be expressed as ΔP = βKΔT, which accounts for the temperature change. This method will yield the correct final pressure based on the given parameters.
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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?
 
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The equation should be $$dV=V\beta dT-V\frac{dp}{K}$$ So, $$\Delta P=\beta K \Delta T$$
 

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