14 matter very cold

What are these objects?

Order them from coldest to hottest

What are these objects?

Order them from coldest to hottest

kT is about how much energy

particles have at temperature T in

kelvin

Worked example

• On a nice summer’s day (27 oC) how much energy would the particles have?

Worked answer

JkT

KJKkTQ

JKk

KCT o

21

123

123

101.4

3001038.1

1038.1

30027

Example questions

• Determine the amount of energy a particle would have if it were:

– In the centre of the Sun– In the centre of a supernova– In Mars’ northern polar cap– In interstellar space

Location k / JK-1 T / K kT / J

Centre of the Sun 1.38 x 10-23

Centre of a supernova 1.38 x 10-23

Within magma 1.38 x 10-23

Within Mars' northern polar cap

1.38 x 10-23

In interstellar space 1.38 x 10-23

Location k / JK-1 T / K kT / J

Centre of the Sun 1.38E-23 1.50E+07 2.07E-16

Centre of a supernova 1.38E-23 1.00E+11 1.38E-12

Within magma 1.38E-23 1.00E+03 1.38E-20

Within Mars' northern polar cap

1.38E-23 2.30E+02 3.17E-21

In interstellar space 1.38E-23 3.00E+00 4.14E-23

If T = 10 000 K

eVkT 1

The eV

• The energy gained by an electron as it moves through a potential difference of 1 V

JW

VCW

QVW

Q

WV

19

19

106.1

1106.1

Show kT = 1eV (T = 10000K)

eVkT

JeV

JkT

KkT

KT

1

106.11

1038.1

100001038.1

10000

19

19

24

Ideal gaskT

2

1

kT2

1

kT2

3 kT2

1

kT2

1

kT2

1

kT2

1

kT3

Hotter and hotter

Life at T = 300 K

Fires and kilns, T = 1500 K

White hot at the Sun’s surface, T = 6000 K

Hotter still: inside the Sun, T = 6000000 K