# How can the piston be pushed outside during an isothermal expansion if the internal pressure is less than the external one?

Let us say we have an ideal gas inside a cylinder closed with a piston. We put the cylinder over a heat bath at temperature $$T_{1}$$ and allow the gas to expand isothermally as bellow (we ignore gravity). We assume that initially the pressure on both sides of the piston is $$P_0$$.

Now, since we have an ideal gas, during each step of the process we must have $$PV=NkT,$$ and since we're considering an isothermal expansion, the equation reduces to $$PV=const.$$ This equation tells us that as the gas is expanding, the pressure inside the cylinder $$P$$ is decreasing, thus we will have $$P But the external pressure $$P_{ext}$$ is actually increasing (or, worst case scenario, remains at the same initial value $$P_{0}$$), thus $$P_{ext}\ge P_{0}.$$

So how can the piston be pushed outside if the internal pressure $$P$$ is less than the external pressure $$P_{ext}$$ during each step of the process?

• It is very hard to follow your equations. Do you know how to use MathJax? I believe a link to a tutorial may be available on this site. Jan 8, 2020 at 23:11
• @BobD But I did use MathJax, you can check it by trying to edit the post. Jan 8, 2020 at 23:13
• Oops! Sorry. I was looking at the your edit in transition. Jan 8, 2020 at 23:14
• @BobD I tried to make it more readable, does it look fine? Jan 8, 2020 at 23:20
• To get the gas to expand isothermally, you need to gradually lower the external pressure (in tandem with the internal pressure). Jan 8, 2020 at 23:20