1. Properties of Matter Thermodynamic Mechanical Work:
PHY1039
Properties of Matter
Thermodynamic Mechanical Work:
1, 2 and 3 Dimensions
(See Finn’s Thermal Physics, Ch. 2)
27 February and March 1
Lectures 7 and 8

2. Types of Work
Mechanical: related to force acting through a distance: our main focus
Electrical: electrical current flowing through a resistor under an applied potential
Capacitive: storing of electric charge under an applied electric field
Magnetic: increasing the magnetic moment of a material with an applied magnetic field
SI Units of work: Nm (also called a Joule, J)

3. Actuator driven by thermal expansion of water and air
Examples of Mechanical Work
Actuator driven by thermal expansion of water and air
Force acting through a distance to do work on surroundings
Change in length, L, under a constant (?) force
Source:
Front cover of Scientific American, Oct. 2003
Work can be done on the system by the surroundings or done by the system on the surroundings.

4. V.H. Ebron et al., Science (2006) 311, 1580
Example of negative linear expansivity being exploited to convert chemical energy into work
A chemical reaction with methanol creates heat in the NiTi alloy wire. At a higher temperature, the wire’s length shrinks - thus lifting a weight and doing work on the surroundings.
V.H. Ebron et al., Science (2006) 311, 1580

5. +F +F Mechanical Work, W, in One Dimension L1 L2 𝑑𝑊=F𝑑𝐿 Initial State
Ask yourself: Is F
constant with changing L? +F L1
If yes:
𝑊=F𝐿=F ( 𝐿 2 − 𝐿 1 )
Final State
T2 > T1
IMPORTANT
Sign Convention:
Positive W: work done on system by surroundings
Negative W: work done on surroundings by the system dL +F L2
Usually dL is +ve when T increases!

6. F=0 +F Isothermal Mechanical Work in One Dimension 𝑊= 𝐿 1 𝐿 2 F 𝑑𝐿
Initial State T1
Ask yourself: Is F
constant with changing L?
(What does the equation-of-state say?)
F=0
(or initial value) L1
If yes:
Final State
𝑊=F𝐿=F ( 𝐿 2 − 𝐿 1 ) T1
If no: must integrate over F(L).
See today’s tutorial. dL +F L2

7. Weak Nano-scale Forces Can be Measured
Atomic force microscope (AFM)
The AFM probe is exceedingly sharp so that only a few atoms are at its tip!
Sensitive to forces on the order of nano-Newtons.

8. Tip for Atomic Force Microscopy
The tip is on a cantilever, which typically has a spring constant on the order of k = 10 N/m.
Modelled as a simple spring:
F = kz
where z is the deflection in the vertical direction.
Radius of curvature ~ 10 nm
Ideally, one of the atoms at the tip is slightly above the others.
AFM tips from NT-MDT. See

9. Doing Work on the Nano-Scale
Pushing on AFM probe tip F
Pulling on the AFM probe tip L

10. Emulsion: Droplet of one liquid dispersed in another
Oil
Interface with a tension of G
Do work on system (e.g. by shaking)
Water
Interface with a tension of G
Oil
Water
Water
Work to create emulsion droplets:
Oil
𝑊= 𝐴𝑜 𝐴 Γ𝑑𝐴
See emulsion droplet formation:

11. Physics of a “Bubble Jet” Printer
Question for Tutorial: How much work is required to create a droplet of ink?

12. F Isothermal Mechanical Work in Two Dimensions ℓ ℓ 𝑑𝑊=F𝑑𝐿=Γℓ𝑑𝐿
For each surface:
Initial State T1
𝑑𝑊=Γ𝑑𝐴
Γ= F ℓ ℓ A1
𝑊= 𝐴 1 𝐴 2 𝑑𝐴 L
Membrane: two sides
Surface: one side only
Ask yourself: Is G
constant with changing A?
Final State T1
If yes: ℓ A2 dA F
𝑊=𝐴=( 𝐴 2 − 𝐴 1 ) dL

13. Surface Tension of Molecular Layers
Langmuir trough
water
G is a function of A! G
Area adjusted with barriers
barrier A

14. F F Isobaric Mechanical Work in Three Dimensions T1 T2 > T1
Initial State
𝑑𝑊=F𝑑𝐿=−𝑃𝐴𝑑𝐿
Isobaric = constant P F A
𝑑𝑊=−𝑃𝑑𝑉
P= F 𝐴 = 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 𝑓𝑜𝑟𝑐𝑒 𝐴𝑟𝑒𝑎 A
𝑊=− 𝑉 1 𝑉 2 𝑃𝑑𝑉 V1 T1
Positive P is pressing inward.
But F pressing inwards is negative!
Final State
Ask yourself: Is P
constant with changing V? F
Only applies to reversible processes! A A V2
+dL
If yes:
𝑊=−𝑃𝑉=−𝑃( 𝑉 2 − 𝑉 1 )
T2 > T1
Question: Is this result consistent with our sign convention?

15. Earth’s Atmospheric Pressure
Isobaric Conditions
Earth’s Atmospheric Pressure
Height (km) Pressure (kPa)
Crab Nebula
Pressure is low but roughly constant!
Isochoric = constant volume. How much work is done in an isochoric process?

16. F Isothermal Mechanical Work in Three Dimensions T1 T1 Initial State A
Isothermal = constant T A A V1 T1
𝑊=− 𝑉 1 𝑉 2 𝑃𝑑𝑉
Apply a pressure to the system and compress it to a smaller V.
Ask yourself: Is P
constant with changing V?
(What does the equation-of-state say?)
Final State F A
-dL A
Work can be done on solid, liquid and gas systems by compressing them.
Work is done on the surroundings by a system when it expands. V2 T1

17. CO Map of the Universe
This is the first-ever all-sky map of carbon monoxide in the cosmos. The Planck space telescope was designed to look at the background glow in the cosmos in an effort to understand how it formed. Coincidentally, scientists have found that it can help to spot star-forming regions where carbon monoxide glows brightly despite its low abundance

18. Adiabatic Free Expansion of a GasV1
Vacuum V2

19. Compressive (Tensile) Force from Thermal Expansion of Beams

20. Applying the “Thermodynamic Method” to Problem Solving
Wire pulled in tension between two walls: T1 F1 F1 L1
Question: What is the increase on the tension of the wire when it is cooled from a temperature of T1 to T2?
(F1, L1, T1)
(F2, L1, T2)