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Work -- Part 1

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Physics 313

Professor Lee Carkner

Lecture 6

1

- Work is force times displacement
- In thermodynamics we will only consider external work
- Involves interaction with another system or its surroundings (external to the system)

2

- Work by the system is negative
- decrease internal energy

- Work done on the system is positive
- increase internal energy

- If one system does work on the other, the sign depends on point of view

3

- Work is not a property of the system
- Neither is heat
- P, V and T are

- Work is a transfer of energy due to a volume change
- Heat is a transfer of energy due to temperature change

4

W = F x

dW = F dx

dW = PA dx

dW = -P dV

- A small volume change (dV) produces a small amount of work (dW)
- If dV is positive (increase in V) then W is negative (work by the system)

5

- To find the total work, integrate dW between the initial and final states:
W = - P dV

- Need to know P as a function of V
- Equation of state

- Need to limit T
- W depends on both the change of volume and how the volume changed

6

- For a change of volume, (Vi, Pi) and (Vf,Pf) can be plotted on a PV diagram
- The process by which the volume changes is a line or curve connecting the two points
- The work is the area under the curve
- For different processes, different curves, different amounts of work

7

- If the system moves from i to f and then back to i, it is a cycle
- If the same path is traveled in both directions, W=0
- if two different paths are traveled W is the area between the curves

8

- What are the paths?
- Isothermal: keep constant T (add or subtract heat)
- follow isotherm

- Isobaric: constant P (add or subtract heat)
- horizontal

- Isochoric: keep constant volume (rigid container, W=0)
- vertical

9

Isobaric (p=const.)

p

Isothermal (T=const)

Adiabatic (Q=0)

Isochoric (V=const)

V

10

- On PV diagram:
- Move to right = compression = positive work
- Move to left = expansion = negative work

11

- Need equation of state and limit on T
- Example: isothermal
- P is replaced with equation of state, T comes out of integral

- Final expression for work in terms of constants and Vi and Vf

12

PV = nRT

P = nRT/V

W = - (nRT/V) dV

W = -nRT (1/V) dV

W = -nRT ln (Vf/Vi)

13

- From equations:
- Find P(V,T)
- Limit T
- Integrate dW
- Check sign

- From PV diagram:
- Find area
- Find sign (V increase (-) or decrease(+))

14