# Thermodynamics-Find final pressure of a piece of lead

In summary: Oh, I think I understand. I was trying to still solve for a value of α but I found there is a standard volumetric thermal expansion coefficient for lead. Thanks!
Problem:
The temperature of a piece of lead is increased from 20C to 35C while its volume is held constant by increasing the hydrostatic pressure. If the initial pressure is 1atm, what is the final pressure?

Honestly, I'm not sure where to begin here. Everything we have done thus far has been in relation to gases and this isn't an ideal gas here.

I know if a volume is constant it is considered a isochoric process and the process does no pressure-volume work. Also, Q=mCvΔT.
But I am not sure where to go from here, much less how to relate this to a process involving a solid.
Any help is much appreciated!

Problem:
The temperature of a piece of lead is increased from 20C to 35C while its volume is held constant by increasing the hydrostatic pressure. If the initial pressure is 1atm, what is the final pressure?

Honestly, I'm not sure where to begin here. Everything we have done thus far has been in relation to gases and this isn't an ideal gas here.
Indeed, not much of a gas! You need to look at thermal expansion coefficients.

Last edited:
DrClaude said:
Indeed, not much of a gas! You need to look at thermal exapansion coefficients.
...and bulk modulus of Pb.

Chestermiller said:
...and bulk modulus of Pb.
So, Bulk modulus of a solid is B=ΔP/(ΔV/V). But if the process is done by keeping the volume constant, that would give B=(Pf-1atm)/0=undefined?

I'm thinking, then, that there is a way to relate volume to temperature?
Volume is related to temp by :ΔV/V=αvΔT where αv= 1/V* dV/dT. I'm not sure if this is how to properly relate the two since you would still have to have a numerical value for V?

So, Bulk modulus of a solid is B=ΔP/(ΔV/V). But if the process is done by keeping the volume constant, that would give B=(Pf-1atm)/0=undefined?

I'm thinking, then, that there is a way to relate volume to temperature?
Volume is related to temp by :ΔV/V=αvΔT where αv= 1/V* dV/dT. I'm not sure if this is how to properly relate the two since you would still have to have a numerical value for V?

Not really. You can use α to get ΔV/V from the temperature rise, and then use B to figure out how much ΔP you need to exactly cancel out the ΔV/V from the temperature rise.

Chestermiller said:
You can use α to get ΔV/V from the temperature rise

How do you go about doing that? Sorry, I'm just not seeing how this fits together yet.

How do you go about doing that? Sorry, I'm just not seeing how this fits together yet.
You wrote the equations yourself in a previous post:

B=ΔP/(ΔV/V)
ΔV/V=αvΔT

Oh, I think I understand. I was trying to still solve for a value of α but I found there is a standard volumetric thermal expansion coefficient for lead. Thanks!

## 1. What is thermodynamics and how does it relate to finding the final pressure of a piece of lead?

Thermodynamics is a branch of physics that deals with the relationship between heat, energy, and work. In this case, it can be used to determine the final pressure of a piece of lead by analyzing the changes in temperature and volume.

## 2. What information is needed to find the final pressure of a piece of lead using thermodynamics?

To find the final pressure of a piece of lead, you will need to know the initial pressure, temperature, and volume of the lead, as well as any changes in those values during the process.

## 3. What is the formula for calculating the final pressure of a piece of lead?

The formula for calculating the final pressure of a piece of lead is P2 = (P1V1T2) / (V2T1), where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

## 4. Can thermodynamics be used to find the final pressure of any material?

Yes, thermodynamics can be used to find the final pressure of any material, as long as the initial and final pressure, temperature, and volume are known or can be measured.

## 5. How can the final pressure of a piece of lead be useful in practical applications?

The final pressure of a piece of lead can be useful in various practical applications, such as in industrial processes, where it is important to know the final pressure of a material in order to ensure the safety and efficiency of the process.

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