Calculating Final Pressure for a Metal Undergoing Temperature and Volume Changes

In summary, a metal with a volume expansivity of 5 x 10^-5 K^-1 and isothermal compressibility of 1.2x10^-11 Pa^-1, initially at a pressure of 1 x 10^5 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. To calculate the final pressure, the problem can be broken down into two steps: first, determining the change in volume during the isobaric temperature increase of 12 K, and second, calculating the change in volume during the isothermal compression to the final volume. The resulting change in pressure
  • #1
zenicorn
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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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  • #2
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?
 

1. How do you calculate the final pressure?

The final pressure can be calculated using the ideal gas law, which states that the product of the gas pressure and volume is equal to the product of the number of moles of gas, the universal gas constant, and the temperature in Kelvin.

2. What information is needed to calculate the final pressure?

To calculate the final pressure, you will need to know the initial pressure, volume, number of moles of gas, and temperature. All of these values must be in consistent units, such as atmospheres, liters, moles, and Kelvin.

3. Can the final pressure be calculated for any gas?

Yes, the ideal gas law can be used to calculate the final pressure for any gas, as long as the gas behaves ideally. This means that the gas particles are not interacting with each other and there are no significant changes in temperature or volume.

4. Can the final pressure be calculated for a gas mixture?

Yes, the ideal gas law can be used to calculate the final pressure for a gas mixture. However, in this case, the number of moles and temperature must be calculated for the entire gas mixture, not just for one component.

5. What are the units for final pressure?

The units for final pressure will depend on the units used for the other variables in the ideal gas law. For example, if the volume is given in liters and the pressure is given in atmospheres, the final pressure will also be in atmospheres.

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