Propane gas (C3H8) behaves like an ideal gas with g = 1.127. Determine the molar heat capacity at constant volume and the molar heat capacity at constant pressure

Video transcript

Hey everyone in this problem. We are told that real gasses can approach the behavior of ideal gasses under certain conditions and that helium is thought to be the closest to an ideal gas with the ratio of heat capacities 1.66. Okay. And we're asked to calculate the molar heat capacities CV and cp of helium. All right. So, let's think about the heat capacity CV and C P K. So CV is the heat capacity with constant volume and cP is with constant pressure. We're told gamma. Okay, well, we know that gamma is going to equal to the ratio of the two. So cP over CV know that gamma is 1.661 point 66 is equal to CP over CV. Which means that we can write C P as 1. C B. Okay, so we know the relationship between the two. If we can find one of them, then we'll be able to find the other. All right, let's also recall that we can write C P is equal to C V plus R K. The gas constant. Alright, so doing this will allow us to find one of these values. Okay, Why? Well, because we can substitute what we know About the relationship here in Blue CP is equal to 1.66 CV into this other equation. Okay, so let's substitute CP is equal to 1.66 CV Into this equation with the gas constant. What we're going to find is that 1.66 CBB is equal to cv plus our I'm just gonna give ourselves some more room to work. So moving the CV to the left hand side we get 0. CV Is equal to R. Which is 8.314 eight jewels per mall Calvin dividing is gonna give us C. V. is equal to .597 jules Permal Calvin. Okay. Or if we round we get 12.6 joules per mole. Well then okay so this is gonna be our value of C. V. Now it's fine. The value of C. P. A. And I mentioned before the ratio between the two gave us the ability to calculate one as long as we found the other. Okay so now that we have Cv we can substitute that in and find cp and we're going to get Cp is equal to 1.66 times C. V. Which is 12.597. Okay, jules per mole Calvin. This is gonna give us c. p. is equal to 20.91 jules per mole. Okay and so that is our heat capacity under constant pressure. 20.91 jewels for both Calvin. And so the answer is going to be answer. C Okay. The heat capacity under constant volume is 12.6 joules per mole kelvin and under constant pressure is 20.91 joules per mole kelvin. That's it for this one. Thanks everyone for watching. See you in the next video