Calculating Final Pressure for a Metal Undergoing Temperature and Volume Changes

[zenicorn]

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.

 

[mjc123]

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?