Why isn't pressure a measure of energy?

Question

Hey guys, I'm having a problem in understanding the 1st Law of Thermodynamics.

If i would increase the pressure of a closed system by compressing a gas in a cylinder isothermal, the 1.Law states, that all the work i put in to the system, i get out by heat.

So my 2.state would be the gas at the same temperature (same internal energy), but compressed (at a higher pressure).

But isn't this compressed gas able to do more work, than the not compressed?
If i drilled a hole in the cylinder my high pressure gas could do some work.

Where does this energy come from, since all my input energy i put in by work, came out in form of heat?

Answer 1

The pressure is higher, but the volume is less. The kinetic energy per particle stays the same, when compressing isothermally, there are just more particles per volume to "bounce on the walls", thus the higher pressure. Your higher pressure gas from your drilled cylinder could just do more work per volume, but since there is less volume available the total work stays the same!

Answer 2

Pressure is equal to force per unit area which equal to energy per unit volume. Hence the work which is done by the pressure is due to the change in pressure and not pressure itself per say.
That is given by Bernoulli's equation.
Here's some more about Bernoulli's equation.

Answer 3

The first law of thermodynamics says $\delta Q = du + \delta w$

For isothermal compression internal energy of the system remain unaltered. Hence $\delta u = 0 $

Hence $\delta Q = \delta w$

All the work $\delta w $ that is done on the system has been released to the outside world as $ \delta Q$ It has no more ability to do work than it had before the compression since all that energy has been already released during the isothermal compression.