Five moles of an ideal monatomic gas with an initial temperature of 127°C expand and, in the process, absorb 1500 J of heat and do 2100 J of work. What is the final temperature of the gas?

Question

Accepted Answer

Hey everyone in this problem. We're told that at a temperature of 30 degrees Celsius, a rubber balloon is filled with three moles of helium. The balloon is left out in the sun to expand helium absorbed joules of heat and does 800 joules of work on the rubber and were asked to determine the final temperature T. F. Of helium. Alright, so we're told information about the heat and the work. Let's recall that we can relate the two through the following delta U. The change in internal energy is equal to Q. The heat minus w The work Now DELTA U. Is not what we're trying to find. We're trying to find the final temperature. But let's go ahead and do this calculation and see if that's going to help us get to that final temperature. So, the heat we have that it absorbs 1000 joules of heat because we have 1000 jewels And then 800 joules of work -800 jules gives us a change in internal energy delta u. of 200 joules. All right now, we have a value for DELTA U. Okay, we have helium which is an ideal gas. And let's recall that we can relate delta U. The change in internal energy to the temperature through the following DELTA U. Is equal to N C V. Delta T. Okay, so we have delta U. The change in internal energy and the number of moles which we know cv the heat capacity at constant volume and delta T. The change in temperature. Okay, so finding DELTA U. Is now going to allow us to use this equation to find that final temperature T. F. Okay. Alright, so again we know Delta U. We know and we're told the number of moles in the question. We know the initial temperature 30°C. We want to find the final temperature. So the only thing missing is CV. Okay, well helium is a mono atomic gas. And let's recall when we have a mono atomic gas tells us that C. V. The heat capacity at constant volume is going to be equal to three halves are okay? Where r is the gas constant? So we do know Cv Okay, so let's plug in our values. We get delta U. Is 200 jewels on the left hand side. Okay? With the number of moles which is three C. V. Which we just found three halves times are the gas constant, which is 8.314. The unit is jewel per mole Calvin eight times delta T. So this is going to be T final which is what we're looking for K. T. F minus T. Initial, which we're told is 30 degrees Celsius. Okay, we're gonna take 30 we're gonna add 273.15 to convert this into Calvin. Okay, we have per Calvin here. So we want the um units for anything related to temperature to be the same. All right, Let's simplify here. So we have our 200 jewels on the left hand side. Okay? We have three more times three half times 8.314 joules per mole kelvin. The unit of mole will cancel. We're gonna be left with 37. jewels per Calvin times. T Final the final temperature we're looking for minus 303.15 Calvin. Alright, we wanna isolate T. F. So we divide by this 37.413. The unit of jewel will cancel. On the left hand side. We're gonna be left with 5. Calvin. And on the right we have T final -303.15 Calvin. Okay, adding the 303.15 to the other side. We get TF the final temperature is equal to .496 Calvin. Okay this is gonna be equal to 496. And we subtract 273.15 to get us back 2°C which gives us a final temperature of 35.3 degrees Celsius approximately. Okay, So that is our final temperature and if you look at our answer choices, we see that we're going to have be the final temperature of helium is 35.3°C. Thanks everyone for watching. I hope this video helped see you in the next one

Five moles of an ideal monatomic gas with an initial temperature of 127°C expand and, in the process, absorb 1500 J of heat and do 2100 J of work. What is the final temperature of the gas?

Verified Solution

Key Concepts

Ideal Gas Law

First Law of Thermodynamics

Monatomic Ideal Gas