I just don't get the exact difference between isothermal expansion and free expansion: in free expansion there is no work done since there is no external external pressure. As to the case of isothermal expansion there is no pressure applied, then how is work said to be done in that case?
[Physics] Difference between Isothermal and Free Expansion
thermodynamics
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The difference is that one expansion is quasi-static (the reversible one) while the other is spontaneous because of a dramatic change of the external constraints (the irreversible one).
In the quasi-static case, you start off indeed in the state where gas pressure equates external pressure. An external operator then slightly decreases the outside pressure so that the gas expands a little bit before reaching very fast a new equilibrium state. You then repeat this procedure as many times as necessary to reach the sought pressure.
If instead you decrease instantaneously and dramatically the outside pressure (you decrease it by, say, a factor 3), then the gas will expand until it reaches equilibrium but in a fashion very very different from that of sum of minutes changes that would be done quasi-statically. As an example, for a start, quantities like internal pressure, temperature etc.. are not even well defined during an irreversible expansion.
At the end of the day, these two very different thermodynamic "trajectories" for your system will result in leading to two different final states (in your adiabatic case). And that's the reason why, the entropy change is not the same in the two cases.
in an isothermal process work is done ryt..then so if work is done dosent it mean that there is a change In internal energy
Remember what internal energy $U$ is. It is the sum:
- of atomic vibrations (sensed as the temperature $T$),
- of chemical bonds or "binding energy" (this includes phase changes from e.g. liquid to solid, where internal energy is lowered but temperature is constant),
- of potential energy (if the object is at a high shelf, it has a "potential" to do work),
- of kinetic energy (only if it moves $K=½mv^2$),
- and others alike.
But, doing work $W$ on an object could e.g. be displacing it sideways a distance $x$ - that is, putting it somewhere else. This would require some force $F$, and:
$$W=F \cdot x$$
In this new position no changes are done in chemical composition, no changes in potential energy, no kinetic energy (it lies still on the table), and no temperature change (since you want it to be a isothermal process). So this is an example of work done with no changes in internal energy.
For an isothermal process temperature has to be constant. After you have displaced (pushed) the box and done work on it, friction might stop it. This would generate heat. For an isothermal process this heat $Q$ has to be removen right away (maybe you use a cooling system or liquid). Now, conservation of energy from thermodynamics means that:
$$\Delta U = Q-W$$
And since - as discussed above - internal energy is unchanged, $\Delta U=0$ and $W=Q$.
Best Answer
That's certainly true, in fact free expansion is an irreversible process in which a gas expands into an insulated evacuated chamber, you can think of it like ann container with a piston and the gas is left to expand in vacuum.
Hence, it is evident that $P_{ext}=0$ during the expansion, so the $W=0$. Now for a ideal gas this process occurs quickly so there is not temperature rise as well, so $dT=0$, so as per first law of thermodynamics $Q=0=W$ and since internal energy is only a function of temperature, so $dU=0$ as well.
So that was for free expansion.
Now for isothermal expansion:
Here if we see and characterise the states after and before isothermal expansion we can see: $$T_1=T_2$$ but other quantities differ,like the external pressure is constant, not necessarily zero.
Hence work done can be given by:
$$W_{1 \rightarrow 2}=- \int_{1}^{2}pdV$$ and as $$p=\frac{nRT}{V}$$
Work done can be given as, $$W_{1 \rightarrow 2}=- \int_{1}^{2}\frac{nRT}{V}dV$$ $$W_{1 \rightarrow 2}=-nRT ln\frac{V_2}{V_1}$$
And hence, work done differs in case of isothermal expansion as compared to that of free expansion.