An ideal gas, and a block of copper, have equal volume of 0.5m^3

In summary, the question discusses an ideal gas and a block of copper with equal volume at 300K and atmospheric pressure. Both are subjected to an increase in pressure and the question asks for the work done on each, taking into account the compressibility of copper. Using the ideal gas equation, the work done on the ideal gas can be found. To find the work done on the copper, the formula for compressibility is used to integrate and the result may differ slightly from the standard answer.
  • #1
blade_090
14
0

Homework Statement



An ideal gas, and a block of copper, have equal volume of 0.5m^3 at 300K and atmospheric pressure. The pressure on both is increased reversibly and isothermally to 5atm.
Find the work done of each if the compressibility of copper is 0.7X10^-6 atm-1

the atmospheric pressure the question said is 1atm?
I understand that i should used the work done formula W = P dV
bt i duno how to link the compressibility with work done
 
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  • #2


Welcome to PF, blade_090! :smile:

Yes, (standard) atmospheric pressure is 1 atm.

And yes, work done is dW = P dV.

Do you have a formula for an ideal gas that links pressure to volume (and temperature)?
And what about a formula for compressibility that links pressure to volume (isothermally)?
 
  • #3


so far what i know about ideal gas equation is
PV = nRT
so i have to find the volume change for the ideal gas
use it on W = P dV and i manage to find work done for ideal gas :)
however i still dun have any clue about work done on copper
and for compressibility:
K = (-1/v)(dV/dP)
im still confused about compressibility of copper...
what is the use of compressibility??
 
Last edited:
  • #4


You can rewrite it as:
dW = PdV = -K Vo P dP.
Now integrate?

(We can treat V as a constant volume Vo, since it's nearly constant.)
 
  • #5


ok i got ur point there...
is that any possible that copper has it own pressure beside the atmospheric pressure??
i found the work done from copper..its 0.443J
bt it is different from the standard answer it gave (0.434J)
 
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  • #6


blade_090 said:
ok i got ur point there...
is that any possible that copper has it own pressure beside the atmospheric pressure??
i found the work done from copper..its 0.443J
bt it is different from the standard answer it gave (0.434J)

I'm not sure what you mean with "its own pressure"?

The copper exerts an opposite pressure to the atmospheric pressure.
When the atmospheric pressure is increased, the copper is compressed and as a result gives a greater opposite pressure such that the balance is maintained.

Your results are pretty close...
What did you use for atmospheric pressure?
 

1. What is an ideal gas?

An ideal gas is a theoretical gas composed of molecules that have negligible volume and do not interact with each other. This means that the molecules do not take up any space and do not attract or repel each other, allowing for simple mathematical models to be used when studying the gas.

2. What is the volume of an ideal gas and a block of copper?

The volume of an ideal gas is determined by its temperature, pressure, and number of molecules. In this scenario, the ideal gas and block of copper have equal volumes of 0.5m^3. This means that at a given temperature and pressure, the number of molecules in the ideal gas is equal to the number of molecules in the block of copper that occupies the same amount of space.

3. How do the properties of an ideal gas and a block of copper differ?

While both the ideal gas and block of copper have equal volumes in this scenario, they differ in other properties. The ideal gas does not have a fixed shape or volume, while the block of copper has a definite shape and volume. Additionally, the molecules in an ideal gas do not interact with each other, while the molecules in the block of copper are held together by intermolecular forces.

4. What is the significance of equal volumes in this scenario?

The significance of equal volumes in this scenario is that it allows for a comparison of the number of molecules in an ideal gas and a solid. It also shows that the volume of a solid may be equal to the volume of a gas at certain conditions, but the properties and behavior of the two substances are still different.

5. Can the volume of an ideal gas and a block of copper change?

Yes, the volume of an ideal gas and a block of copper can change. In the case of an ideal gas, its volume is directly proportional to its temperature and inversely proportional to its pressure. As for the block of copper, its volume can change when subjected to different temperatures or pressures, but its shape and volume will remain constant under a given set of conditions.

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