Isothermal Expansion: Explained

[Fibo112]

I am a little confused by the following; When an isothermal expansion takes place there is negative work done on the gas by the pressure, this I understand. Now by the first law the change in internal energy is equal to the heat transferred to the gas plus the work done it. So now in my script is says that for this isothermal expansion to take place there must be heat transferred to the gas(in the same amount of the negative work done). Now this means that the internal energy of the gas at the end is equal to the internal energy at the beginning right? This doesn't really make sense to me. Wouldn't a large volume of gas have more energy than a small volume of gas at the same temperature? I hope this question makes sense.

 

[Charles Link]

You have a larger volume of gas, but if you consider the ideal gas law, $PV=nRT$, the pressure must be reduced. Alternatively, since the gas has expanded, the density $n/V$ is reduced, and also the energy density. $\\$ At the same temperature, the individual gas molecules have the same distribution of velocities, so if you sum the total of $E=(1/2)mv^2$, you will get the same result for both volumes. For an ideal monatomic gas, the internal energy $U=\frac{3}{2} nRT$ independent of the volume.

 

[Delta2]

This is where we allow sometimes our intuition to fool us (larger volume hence more energy?!?), but it is a well know result that which Charles says that the internal energy depends only on temperature and not on volume (that is for the case of an ideal monoatomic gas, our intuition might not be completely wrong if the gas is not ideal it might depend on volume or other things as well).