A gas with initial state variables p₁, V₁ , and T₁ expands isothermally until V₂=2V₁. What are and (b) p₂?

Video transcript

Hello, fellow physicists today, we're going to solve the following practice problem together. So first off, let's read the problem and highlight all the key details that we need to use to find our final solution. So an ideal gas has a pressure P zero volume V zero and temperature T zero, the gas expands through an isothermal process to point V one equals three V zero. Find P one the pressure at V one. Awesome. So we have the following multiple choice answers to choose from. So A is P zero unchanged B is P zero divided by three C is three P zero and D is 1.1 P zero. OK. So at the bat, we should recall that is. So thermal conditions means that the temperature is constant. So isothermal equals constant temperature. So if the temperature, the temperature T equals constant, then we can write the following mathematical statement that the final temperature T one is equal to the initial temperature T zero. So final temperature T one is equal to the initial temperature T zero. OK. So now we need to recall our handy dandy ideal gas law. So the ideal gas law is PV equals lower case N RT where N is the number of substance and R is the ideal gas constant. OK. So also it's important to note that N R is a constant value. So rewriting our ideal gas law with, you know, isolating N R by itself will get that N R equals PV divided by T. So considering here we'll box it in green. So considering this mathematical statement or I should say, considering this above relation, we could write the following equation. We'll write it in blue. So we can say for equation one that P zero times V zero divided by T zero equals P one V one divided by T one. OK. So due to it being an isothermal process, that means that the temperature, the change in temperature will remain constant. And because of this fact, we could take equation one and write equation two as such, we could write it as P zero times V. I should say P zero multiplied by V zero equals P one multiplied by V one. So now we need to rewrite equation two to solve for P one, the final pressure. So solving for the final pressure by itself would be P one equals P zero times V zero divided by V one. So when we plug in the value for V one, which in the equation again, the given practice from it said that V one equals three V zero. So let's write that down. So P zero multiplied by V zero divided by three V zero. So when we solve for this, the V zeros cancel out. So our final answer will be P zero divided by three. So the final answer will be B P zero divided by three. So thank you so much for watching. I can't wait to see you in the next video. Bye.