Ideal gases: irreversible transformation

In summary: The pressure of the water is depth dependent, but the pressure of the balloon is not. It's always the same at h_{2}.
  • #1
armandowww
78
0
A balloon featured with a negligible thermal capacity contains [tex]V_{l}=3l[/tex] of ideal gas and is immersed in a lake (thermal bath) at the depth of [tex]h_{l}=10m[/tex] beneath the lake surface. If it is brought to the depth of [tex]h_{l}=3m[/tex], how much is the heat exchange?
 
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  • #2
I did 2 typos. The first [tex]h_{l}[/tex] has to be replaced with [tex]h_{1}[/tex] and the second with [tex]h_{2}[/tex]... anyway, could you help me please? Thanks
 
  • #3
Sounds like a case of isothermal expansion.
 
  • #4
yes, it is. But I don't know how to calculate that heat...
 
  • #5
Remember that for an isothermal expansion, the internal energy doesn't change, so work done is equal (up to a sign) to the heat transfer. Now, what's the work done by the gas in the expansion?
 
  • #6
I was just arrived to this same conclusion. But now, about work integral [tex]W=\integral_{V_{1}}^{V_{2}}p_{ext}dV[/tex], what is the correct expression I have to use for external pressure? I supposed it is a constant because of fast rising. But what's the value?
 
  • #7
[tex]W=\int_{V_{1}}^{V_{2}}p_{ext}dV[/tex]
 
  • #8
I'd expect that the internal pressure equals the external pressure. As it's isothermal, that also allows you to work out the volume. You should get an integral involving 1/V, and so some logs out the end.
 
  • #9
Surely you'd be right if transformation could be thought as a reversible transformation (a nearly static one). I learned that heat exchange and work done by the system are not function of state and are strictly dependent upon the particular path the transformation has gone across.
 
  • #10
Isothermal expansion is reversible
 
  • #11
The equation of state [tex]PV=nRT[/tex] keeps always its validity, but the reversibility is not a prerequisite at all. If transformation takes place with rapidity, alas, your last sentence is not satisfactory anymore.
 
  • #12
Okay, that is true. However, assuming that in moving the balloon doesn't put significant amounts of energy into the system, the answer will be the same as if the entire process happened quasi-statically.
 
  • #13
I was told that the correct calculation is given by using as [tex]p_{ext}=const[/tex]. Nevertheless, this constant is the external pressure corresponding to [tex]h_{2}[/tex]! This is the incomprehensible enigma I'm stuck in!
 
  • #14
I don't see why the external pressure is constant -- pressure of the water would be depth dependent.
 

Related to Ideal gases: irreversible transformation

What is an ideal gas?

An ideal gas is a theoretical gas that follows the ideal gas law, which states that the pressure, volume, and temperature of a gas are all directly proportional. This means that as one of these variables changes, the others will also change in a predictable manner. Ideal gases do not exist in reality, but they serve as a useful model for understanding the behavior of real gases.

What is an irreversible transformation?

An irreversible transformation is a process in which a system changes from one state to another, but cannot be reversed by any means. In other words, the system cannot return to its initial state after the transformation. This is often due to the dissipation of energy, such as heat, during the process.

What happens to an ideal gas during an irreversible transformation?

During an irreversible transformation, an ideal gas will experience a change in its pressure, volume, and temperature. However, the relationship between these variables will no longer follow the ideal gas law. This is because irreversible transformations involve the dissipation of energy, which affects the behavior of the gas.

Why are irreversible transformations important in studying ideal gases?

Irreversible transformations are important because they allow us to observe and understand the behavior of real gases, which do not always follow the ideal gas law. By studying irreversible transformations, we can gain insight into the factors that affect the behavior of gases, such as energy dissipation and intermolecular forces.

What are some examples of irreversible transformations in ideal gases?

Some examples of irreversible transformations in ideal gases include the expansion of a gas into a vacuum, the compression of a gas in a piston-cylinder system, and the mixing of two gases. In all of these cases, energy is lost in the form of heat, and the gas undergoes irreversible changes in pressure, volume, and temperature.

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