Calculating Final Pressure in Isochoric Thermo Process

[s7b]

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?

 

[Chestermiller]

The equation should be $$dV=V\beta dT-V\frac{dp}{K}$$ So, $$\Delta P=\beta K \Delta T$$