A cylinder contains 0.100 mol of an ideal monatomic gas. Initially the gas is at 1.00 * 10^5 Pa and occupies a volume of 2.50 * 10^-3 m^3. (b) If the gas is allowed to expand to twice the initial volume, find the final temperature (in kelvins) and pressure of the gas if the expansion is (i) isothermal; (ii) isobaric; (iii) adiabatic.

Video transcript

Hey everyone in this problem. We have a balloon volume 0.32 m cubed. It contains an ideal gas at a pressure of 1.2 times 10 to the five pascal's. Okay. We're told the number of moles in the balloon is 0.12. And that the balloon expands to 1.8 times the original volume. They were asked to calculate the final temperature in Calvin and the pressure and were told to assume Aisa barrick process. Alright, So let's start with that ice a barrick process. If we have an ice a barrick process. Okay, this means that we have constant pressure. All right. So if we have constant pressure while then p to the final pressure that we want to find is just gonna equal the initial pressure P. One. Okay. Which is going to be 1.2 times 10 to the five pascal's. Okay. Alright. So we found the final pressure by just considering what type of process we have. Okay. And now we're also asked to find the final temperature. So we have some information about the pressure about the volume and we want to find the temperature. Okay, So let's recall our ideal gas law. Okay, we're told that we have an ideal gas here so we can use the ideal gas law and it's gonna tell us that we have PV is equal to N. R. T. Okay. In this case we want to find the final temperature we'll call it t. two. So we're gonna use the final pressure in the final volume. Okay, these all need to be at the same measurement at the same time point. Okay. Alright. So we know the pressure, We know the volume. And what is this end while N. Is the number of moles. Okay. We're told that. So we have N. R. Is r gas constant. So we're okay to go ahead, substitute our values to find T two. So the final pressure when we just found that 1.2 times 10 to the five pascal's our final volume. Okay, We're told that it's 1.8 times the original volume. Okay, so this is going to be 1.8 Times the original volume, which is 0.0032 m cubed. 1.8 times 0.0032 m cubed. And on the right hand side, we have and the number of moles which are told is 0. Times are and that's more times are which is the ideal gas constant. 8.314 jules per mole Calvin eight times the temperature. T two. Alright, so the unit of mole will cancel with the Permal here. Okay, on the left hand side we're going to get 691.2 K. We have pascal meters cubed which is the unit jewel. Okay, on the right hand side we get 0.99768. Again. The unit per mole canceled. So we're just left with jewel per Calvin K times T two. And then when we divide the unit of jewel will cancel we're gonna be left with T. Two is equal to 692. Calvin. Okay. And rounding we're going to get 693 Calvin. So that is the final temperature we were looking for. Okay. So we have, the final temperature is 693 Calvin. The final pressure is 1.2 times 10 to the five pascal. So we have answer D. That's it for this one. I hope this video helped see you in the next one.