Consider 2.00 mol of an ideal gas that is taken from state A(PA=. .2.00 atm, VA=10.0 L) to st

Consider 2.00 mol of an ideal gas that is taken from state...

Consider $2.00 \mathrm{~mol}$ of an ideal gas that is taken from state $A\left(P_{A}=\right.$ $\left.2.00 \mathrm{~atm}, V_{A}=10.0 \mathrm{~L}\right)$ to state $B\left(P_{B}=1.00 \mathrm{~atm}, V_{B}=30.0 \mathrm{~L}\right)$ by two different pathways: Calculate the work (in units of J) associated with the two pathways. Is work a state function? Explain.

Consider $2.00 \mathrm{~mol}$ of an ideal gas that is taken from state $A\left(P_{A}=\right.$ $\left.2.00 \mathrm{~atm}, V_{A}=10.0 \mathrm{~L}\right)$ to state $B\left(P_{B}=1.00 \mathrm{~atm}, V_{B}=30.0 \mathrm{~L}\right)$
by two different pathways:
Calculate the work (in units of J) associated with the two pathways. Is work a state function? Explain.

Key Concepts

Thermodynamic Work

Thermodynamic work is the energy transferred when a force causes a displacement. In the context of gases, work is often associated with volume changes at a given pressure and is calculated as the integral of pressure with respect to volume, that is, ?PdV. This concept is fundamental in understanding energy exchanges in thermodynamic processes.

Path Dependence

A key idea in thermodynamics is that work is a path function, meaning its value depends on the specific process or path taken between two states rather than solely on the initial and final states. This contrasts with state functions, which depend only on the state of the system. Recognizing path dependence is essential when comparing different process pathways in energy calculations.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and amount of gas. This relationship allows the prediction of a gas's behavior under various conditions. It plays a crucial role in calculating quantities like work, especially when integrating over processes that involve changes in pressure and volume in a predictable manner.

Transcript

00:01 So there's a couple of ways of thinking about how much work is happening here.

00:05 So we have two different paths to go from a to b, one of them defined by these green arrows right here, and the other one by the red arrows.

00:15 Now, the work graphically on this p versus v diagram is all the area below the curve.

00:26 So for the green path, it's all of this area.

00:30 So right here.

00:34 This is all the area below the curve.

00:37 This is the work.

00:38 For the red path, it's not just the area within the box, but also the area below.

00:45 Now, the way we know this formulatically is that the work for a volume expansion at constant pressure is negative p delta v.

00:57 Now, in this case, the change in volume is always going from 30 liters to.

01:04 From 10 liters to 30 liters and so delta v equals 20 liters it's the external pressure that it's going against that's different for the green path right here the pressure externally is one atmosphere and for the other path up here the pressure externally is two and so we can see immediately that these two that the work is not going to be the same and that we before we actually do calculations, that can tell us the answer, is it a state function? no.

01:43 Because a state function would result in the fact that going from this position to that position would be the same no matter what.

01:51 But work is not a state function.

01:53 So it depends on how we got there.

01:55 For example, if we got to be by some crazy path like this, the work would be different.

02:03 And this, that means it's not a state state function...

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