Thermodynamics

I. Temperature

1. Thermal equilibrium. Zeroth law of thermodynamicsa) We need a thermometer

b) Thermal equilibriumc) Zeroth law: If C is in thermal equilibrium with both A and B, then A and B are also in thermal equilibrium with each otherd) Temperature Two systems are in thermal equilibrium if and only if they have the same temperature

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Question: Two thermometers are in thermal equilibrium with each other. One reads in ˚C and one reads in ˚F. At what temperature do they read the same number? That is, at what temperature is TC = TF?

40 3232

595

9

TTT

TTT

TT

CF

CF

2. Temperature scales

TC: 0°C - freezing of water, 100°C - boiling of water

3295 FC TT

15.273

3259

CK

CF

TT

TT

2

3. Thermal expansion

T0, L0

ΔL = α L0ΔT

+ ΔL T = T0 + ΔT, L = L0

L = L0 (1 + α ΔT)

ΔV = β V0ΔT

V = V0 (1 + β ΔT) V=L3

LL

β = 3α

ΔA = 2 α A0ΔT

A = A0 (1 + 2 α ΔT)

A=L2L

L

3

TLTTLTLLA 21211 20

220

20

2

α – linear coefficient of thermal expansion

β – volumetric coefficient of thermal expansion

Question 2: A donut shaped piece of metal is cooled and its temperature decreases. What happened with inner and outer radii after cooling?

Both radii decrease!

Example: An aluminum flagpole is 30 m high. By how much does its length increase as the temperature increases by 20°C? For aluminum the linear coefficient of thermal expansion is 25x106(1/˚C).

ΔL = α L0ΔT

ΔL - ?

4

Question 1: A steel measuring tape is 10.000 m long at 20.0 ˚C.The increase in length of the measuring tape upon heating to 40.0 ˚C is ___ mm. For steel, = 1.2 x 105(1/˚C)

A) 0.8B) 1.6C) 2.4D) 3.2

)/1(1025

20

30

6

0

C

CT

mL

cmmCmCL 5.1105.12030)/1(1025 26

1. Isotherms (Boyle’s law): T=const

II. Ideal gases

nRTPV RTm

PV

)/(31.8 KmolJR

Equation of state

n = m/μ

PV=const

P1V1= P2V2

T1

T2 > T1

V

P

2

22

1

11

T

VP

T

VP

constT

PV

n - number of molesm - total mass of gasμ - molar (atomic) mass (“weight”)

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2. Isobars (Charles’s law): P=const V/T=constV1/T1= V2/T2P1

P2 > P1

T(K)

V

3. Isochors (Gay-Lussaec ): V=const

P/T=constP1/T1= P2/T2

V1

V2 > V1

T(K)

P

T(C)

V

-273.15°C

T(°C)

P

-273.15°C 0°C

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Example 1: The temperature of an amount of an ideal gas has been increased twice, while the volume has been increased four times. What happened with the pressure?

1

11

2

22

T

VP

T

VP

T2 = 2T1

V2 = 4V1

P2 /P1 - ?

2

12

4

1

1

2

2

1

1

2 T

T

V

V

P

P

21

2

PP

Example 2: What is the volume of 1 mole of an ideal gas at “standard temperature and pressure”?

n = 1 molT = 273 K (0° C)P = 1 atm = 1.013x105 Pa

V - ?

K) J/(mol 8.31 R nRTPV PnRTV /

LmV 4.22104.22 33

7

In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold).

Heating a body, such as a segment of protein alpha helix, tends to cause its atoms to vibrate more, and to cause it to expand or change phase.

http://en.wikipedia.org/wiki/Temperature

The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move.

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