Calculate the internal energy change for each of the...

Calculate the internal energy change for each of the following. a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases $23 \mathrm{J}$ of heat. b. A piston is compressed from a volume of $8.30 \mathrm{L}$ to $2.80 \mathrm{L}$ against a constant pressure of $1.90 \mathrm{atm}$. In the process, there is a heat gain by the system of 350. $\mathrm{J}$. c. A piston expands against $1.00 \mathrm{atm}$ of pressure from $11.2 \mathrm{L}$ to $29.1 \mathrm{L}$. In the process, $1037 \mathrm{J}$ of heat is absorbed.

Transcript

00:01 So for all of these questions, you're trying to find the change in internal energy.

00:04 So for part a, we're told that we have 100 joules of work.

00:11 Now we figure out it's positive or negative.

00:13 So they're saying the work is required to compress the gas.

00:17 So this gas is the system.

00:20 So it needs the work to be performed from the surroundings onto the system.

00:27 So when the work is being done by the surroundings onto the system, work is positive.

00:33 Then it says that we have a heat or cue of 23 joules.

00:41 And we were told that the gas is releasing that heat.

00:45 So if the system is releasing heat to the surroundings, it's losing that heat.

00:50 So it's going to be a negative.

00:51 Then we're going to use the equation where the change in internal energy is equal to cue the heat plus w the work.

00:58 So now we just solve for the change in energy.

01:02 So energy is equal to q.

01:04 So we have negative 23 joules plus the work, which is a positive 100 joules.

01:11 Put that into your calculator and you should get 77 joules.

01:17 Now for part b, we are told that we have a piston where the volume compresses.

01:25 So we have an initial volume of 8 .3 liters and a final volume of 2 .8 liters.

01:34 The pressure is constant at 1 .9 atmospheres, and that the heat involved is 350 joules.

01:48 And then we were told that the heat is being gained by the system.

01:51 So if it's gaining the heat, then it's going to be positive 350 joules.

01:56 So now we will still apply the same formula.

02:00 We have our cube, but now we need to solve for.

02:03 Work w.

02:04 So we can use another equation where work is equal to the negative pressure times the change in volume, which is the final volume minus the initial volume.

02:15 So our work is going to be equal to negative the pressure, 1 .9 atmospheres, times the change in volume.

02:23 So the final volume, 2 .8 liters minus the initial volume of 8 .3 liters.

02:29 Type that in your calculator, 2 .8 minus 8 .3.

02:33 Times a negative 1 .9.

02:36 And you should get 10 .45 liters times atmospheres.

02:43 Now, first, before we add it to the heat, we got to make sure they're the same jule, same units.

02:47 So we need to convert the liters to atmospheres into jules.

02:51 So we can say we have 10 .45 liters times atmospheres...

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