Calculating Final Pressure for a Metal Undergoing Temperature and Volume Changes

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To calculate the final pressure of the metal after temperature and volume changes, the discussion emphasizes a two-step approach. First, an isobaric temperature increase of 12 K leads to a change in volume, which can be determined using the metal's volume expansivity. Next, an isothermal compression occurs to account for the increase in volume of 0.5 cm³, affecting the final pressure. The initial pressure of 1 x 10^5 Pa must be adjusted based on the changes calculated in both stages. This method ensures accurate results by addressing both thermal expansion and volume changes systematically.
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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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