- #1

zenterix

- 689

- 83

- Homework Statement
- For a closed system the 1st law in differential form is

$$dU=\delta Q+\delta W\tag{1}$$

- Relevant Equations
- For a reversible process we have

$$\delta Q_{rev}=TdS\tag{2}$$

$$\delta W_{rev}=-PdV\tag{3}$$

and so

$$(dU)_{rev}=TdS-PdV\tag{4}$$

For an irreversible, closed system we have

$$(dU)_{irrev}=\delta Q_{irrev}+\delta W_{irrev}\tag{5}$$

My question is about the following statement

Sure, internal energy is a state function. I still don't understand, however, what it means to have a differential change in an irreversible process.

Here is my understanding right now.

##U## of a closed system is a state function of two of the variables ##P,V,## and ##T##.

However, from what I understand, implicit in this function existing is the notion that the system is in equilibrium so that the variables ##P,V,## and ##T## are actually defined for the system.

Suppose we have a Joule expansion occurring in a closed system of volume ##V## which is split into two volumes ##V_1## and ##V_2##. The gas is initially in volume ##V_1## and then suddenly fills volume ##V_2##.

What does equation (6) mean in this context?

and so

$$(dU)_{rev}=TdS-PdV\tag{4}$$

For an irreversible, closed system we have

$$(dU)_{irrev}=\delta Q_{irrev}+\delta W_{irrev}\tag{5}$$

My question is about the following statement

Because the internal energy is a state function we can write

$$(dU)_{irrev}=(dU)_{rev}=TdS-PdV\tag{6}$$

or

$$dU=TdS-PdV\tag{7}$$

Sure, internal energy is a state function. I still don't understand, however, what it means to have a differential change in an irreversible process.

Here is my understanding right now.

##U## of a closed system is a state function of two of the variables ##P,V,## and ##T##.

However, from what I understand, implicit in this function existing is the notion that the system is in equilibrium so that the variables ##P,V,## and ##T## are actually defined for the system.

Suppose we have a Joule expansion occurring in a closed system of volume ##V## which is split into two volumes ##V_1## and ##V_2##. The gas is initially in volume ##V_1## and then suddenly fills volume ##V_2##.

What does equation (6) mean in this context?