A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110 m^3 of air at a pressure of 0.355 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.390 m^3. If the temperature remains constant, what is the final value of the pressure?

Video transcript

Hey everyone in this problem. We have a piston cylinder assembly, cave an engine. It initially contains half a mole of an ideal gas at a pressure of one atmosphere. The gas inside the cylinder expands slowly. Ice author Mickley until the volume of the cylinder is doubled. Okay, we're asked to find the final pressure inside the cylinder. Alright, so we're thinking here, we have pressure volume and the relationship. Okay, so we have an ideal gas. So let's use the ideal gas law or the ideal gas equation. Okay, we know that we have P. V. Is equal to N R. T. Can you recall that? This is the ideal gas equation? And we have two situations we have before that gas expands and we have after that gas expands. Okay, so we have the initial pressure, the initial volume. Okay, N R T. We have the final pressure, final volume. We go to N R. T. Okay, you don't notice I didn't put subscript on this. N R. T. But why is that? Well, we're told that this expands ice a thermally. Okay, so we know that the temperature stays the same. We don't change the temperature. Okay, so the big T temperature is the same and we have N R N. R is going to be constant as well because we have the same amount of an ideal gas. Okay, so what this means is because N. R. T. Is the same in each of these. N R. T. Constant. Okay, we can set these equal to each other. So we get P I. V. I. Is equal to N R. T. Which is equal to P F V F. Okay. All right well what's the initial pressure? We do know the initial pressure. Okay. It's one atmosphere. We don't know the initial volume. We know it contains half a mole but we don't know the volume. We want to find the final pressure and we don't know the final volume. What do we know though? Let's write out what we know. We know that the final volume is double. The volume of the cylinder is doubled. So the final volume is going to be two times the initial volume. Okay, well this means that the final pressure p that we're looking for can be written as the initial pressure. The initial volume divided by two times the initial volume. Okay. Here the unit or the, sorry, the volume initial will cancel. We're just left with the initial pressure divided by two. We know the initial pressure is one atmosphere Divide by two. And so we get our final pressure of 0. Atmospheres. Okay. And so that's going to be answered. A final pressure is 0.5 atmosphere. That's it for this question. I hope this helped see you in the next video