If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003°C and the pressure is 92 atm?

Video transcript

Welcome back everybody. We are taking a look at a weather balloon that is still in Earth's atmosphere and we are told that the volume while it is in Earth's atmosphere is one m cubed. And it is under standard conditions for Earth, meaning that it has a pressure of 1 80 M And a temperature of Kelvin. Now we are told that it floats up and it's placed right outside of a Martian station where the pressure outside of Mars is going to be six Pascal's and have a temperature of -60°C. And we are tasked with finding what is the new volume as it is parked right outside of the Martian station. Well, first thing that pops out to me, we have volumes, pressures, temperatures, we are going to be dealing with the ideal gas law, which states that pressure times volume is equal to the number of moles times the ideal gas constant, times temperature. Now, since we are given volume, pressure and temperature, I'm actually going to move all of that to one side of our equation. And now that we've done that, it doesn't say anything about the number of moles changing and ours just a constant. So we can assume that the right side of this equation is just a constant, which allows us to set up a new system of equations here. We can say that since the number of moles in the r is not changing. We can say that the pressure of Earth times the volume Earth divided by, sorry, the volume of the balloon in Earth's atmosphere divided by the temperature of the balloon in Earth's atmosphere equal to pressure outside the martian station. The volume outside the martian station, all divided by the temperature outside of the martian station. We are trying to find this volume right here. So I need to isolate that term and here's how I'm gonna do it. I'm gonna multiply both sides by the temperature. Outside the martian station, divided by the pressure. Let's see. I'll do that on this side as well. What you do to one side, you must do to the other. These terms are going to cancel out and we are left with an isolated formula for our volume. So we have found that the volume of the balloon outside the martian station is equal to the volume of Earth times the ratio of the two pressures times a ratio of the two temperatures. So let's go ahead and plug in all the values that we know, volume of the balloon in our atmosphere is one m. Cute pressure is 1 80 M. But I need these units to be the same. So I'm actually gonna convert this to pascal's in 1 80 M. There's 1.13 times 10 to the fifth pascal's. This is divided by pressure right outside the Martian station which is Pascal's and then this is times Be temperatures but I need these to be the same unit. So I'm actually going to convert the temperature right outside the Martian station. So we take our C temperature measurement and then we add 273.15 to get Alvin. This is divided by 273 Calvin. And when we plug all of this into our calculator, you'll notice that these units will cancel out, leaving us with our desired units. And we get that the volume of the balloon right outside the martian station is 100 and 31.8 m cubed, which corresponds to our final answer choice of C. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.