13 Temperature and Ideal Gases

• Homework:

• Problems: 1, 7, 41.

• Thermal Equilibrium

• Temperature Scales

• Ideal Gases

• Thermal Expansion

1

22

Temperature

• T ~ avg. KE/molecule

• Thermal Expansion

• Scales:

• Kelvin, K

• C° = K – 273

• F° = (9/5)C° + 32

Thermal Equilibrium

• Heat flows from hotter object to cooler object.

• When the heat flow ceases the objects are in thermal equilibrium.

• Objects in thermal equilibrium are at the same temperature.

• /

3

Ideal Gas

4

1

11

2

22 :gas ideal confined a of states ComparingT

VP

T

VP

re temperatu x volumepressure

:Equation Gas Ideal

TPV

068.11

1

20273

40273

:offactor aby increases pressure The 40C. to20C

from olumeconstant vat heated is gas idealAn

2

1

1

2

1

2

V

V

T

T

P

P

5

Gas Thermometer

• PV ~ NT• P ~ T (V, N constant)

• Gas cools,

• avg. KE 0,

• (absolute zero),

• P 0,

• ≈ -273 °C

6

Constant Pressure

• What % increase in V occurs for an ideal gas heated from 20C to 40C? (V ~ T)

• (It does not double, b/c C is not a thermodynamic temperature scale)

• V2/V1 = T2/T1 = (273+40)/(273+20) = 1.068

• 6.8% increase in volume.

7

L = Lo T

Linear Thermal Expansion

Example: 100C increase in Aluminum causes a fractional increase in length of 0.0024 = 0.24% change.

8

Bi-Metallic Strips

Summary

• Thermal Equilibrium

• Temperature Scales

• Ideal Gases

• Thermal Expansion

9

1010

Water Expansion• Expansion from 4°C to 100°C (normal)• Contraction from 0°C to 4°C. (anomalous,

transient ice melting)

1111

12

Superheating

• Mythbusters

12

Ideal Gases

• N molecules (few intermolecular collisions)

• v = average speed

• P due to wall-collisions (P ~ Nv/t)

• t = time between same-wall collision

Lvt 2

v

Lt

2

Ideal gas pressure

A

FP

t

v

A

Nm

A

tvNm

A

FP

/

vmFt

tvmF /

(elastic) 2vv

t

v

A

NmP

2

vLt /2

vL

v

A

Nm

/2

2

AL

Nmv2

Ideal Gas Law

t

v

A

NmP

2

vL

v

A

Nm

/2

2

AL

Nmv2

AL) (V KE), avg. ~ (T ~ V

NTP

NTPV ~