67
Energy Balance

# Energy Balance. HEAT TRANSFER PROCESSES Conductive heat transfer Convective heat transfer Radiation heat transfer

Embed Size (px)

Citation preview

Energy Balance

HEAT TRANSFER PROCESSES

• Conductive heat transfer

• Convective heat transfer

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

visiblelight

0.7 to 0.4 m

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelight

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelightinfrared

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelightinfraredmicrowaves x-rays

Electromagnetic Spectrum

(m)

1000 100 10 1 0.1 0.01

ultravioletvisiblelightinfraredmicrowaves x-rays

HighEnergy

LowEnergy

Blackbody radiation—radiation emitted by a body that emits (or absorbs) equally well at all wavelengths

1) All objects emit radiant energy.

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects.

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object.

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects. The amount of energy radiated is proportional to the temperature of the object raised to the fourth power.

This is the Stefan Boltzmann Law

E = T4

E = total radiant energy emitted per unit time per unit surface area(W/m2)

T = temperature (K) = 5.67 x 10-8 W/m2K4 (a constant)

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.

3) The hotter the object, the shorter the wavelength () of emitted energy.

1) All objects emit radiant energy.

2) Hotter objects emit more energy than colder objects (per unit area). The amount of energy radiated is proportional to the temperature of the object.

3) The hotter the object, the shorter the wavelength () of emitted energy.

This is Wien’s Law

max 2828 m T(K)

Stefan Boltzmann Law.

F = T4

F = flux of energy (W/m2)T = temperature (K) = 5.67 x 10-8 W/m2K4 (a constant)

Wien’s Law

max 2828 m T(K)

We can use these equations to calculate properties of energy radiating from the Sun and the Earth.

6,000 K 300 K

Solar Radiation and Earth’s Energy Balance

Planetary Energy Balance

• We can use the concepts learned so far to calculate the radiation balance of the Earth

Some Basic Information:

Area of a circle = r2

Area of a sphere = 4 r2

Energy Balance:

The amount of energy delivered to the Earth is equal to the energy lost from the Earth.

Otherwise, the Earth’s temperature would continually rise (or fall).

Energy Balance:

Incoming energy = outgoing energy

Ein = Eout

Ein

Eout

How much solar energy reaches the Earth?

How much solar energy reaches the Earth?

As energy moves away from the sun, it is spread over a greater and greater area.

How much solar energy reaches the Earth?

As energy moves away from the sun, it is spread over a greater and greater area.

This is the Inverse Square Law

So = L / area of sphere

So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2

4 x x (1.5 x 1011m)2

So is the solar constant for Earth

So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2

4 x x (1.5 x 1011m)2

So is the solar constant for Earth

It is determined by the distance between Earth (rs-e) and the Sun and the Sun’ luminosity.

Each planet has its own solar constant…

How much solar energy reaches the Earth?

Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re)

Einre

How much solar energy reaches the Earth?

Assuming solar radiation covers the area of a circle defined by the radius of the Earth (re)

Ein = So (W/m2) x re2 (m2)

Einre

How much energy does the Earth emit?

300 K

How much energy does the Earth emit?

Eout = E x (area of the Earth)

How much energy does the Earth emit?

Eout = E x (area of the Earth)

E = T4

Area = 4 re2

How much energy does the Earth emit?

Eout = E x (area of the Earth)

E = T4

Area = 4 re2

Eout = ( T4) x (4 re2)

(m)

1000 100 10 1 0.1 0.01

Earth Sun

Hotter objects emit more energy than colder objects

(m)

1000 100 10 1 0.1 0.01

Earth Sun

Hotter objects emit more energy than colder objects

E = T4

(m)

1000 100 10 1 0.1 0.01

Earth Sun

Hotter objects emit at shorter wavelengths.

max = 2828/T

Hotter objects emit more energy than colder objects

E = T4

How much energy does the Earth emit?

Eout = E x (area of the Earth)

Eout

How much energy does the Earth emit?

Eout = E x (area of the Earth)

E = T4

Area = 4 re2

Eout = ( T4) x (4 re2)

Eout

How much solar energy reaches the Earth?

Ein

How much solar energy reaches the Earth?

We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).

Einre

How much solar energy reaches the Earth?

We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).

Ein = So x (area of circle)

Einre

So = L / (4 rs-e2) = 3.9 x 1026 W = 1370 W/m2

4 x x (1.5 x 1011m)2

So is the solar constant for Earth

It is determined by the distance between Earth (rs-e) and the Sun and the Sun’s luminosity.

Remember…

How much solar energy reaches the Earth?

We can assume solar radiation covers the area of a circle defined by the radius of the Earth (re).

Ein = So x (area of circle)

Ein = So (W/m2) x re2 (m2)

Einre

How much solar energy reaches the Earth?

Ein = So re2

BUT THIS IS NOT QUITE CORRECT!

**Some energy is reflected away**

Einre

How much solar energy reaches the Earth?

Albedo (A) = % energy reflected away

Ein = So re2 (1-A)

Einre

How much solar energy reaches the Earth?

Albedo (A) = % energy reflected awayA= 0.31 today

Ein = So re2 (1-A)

Ein = So re2 (0.69)

reEin

Energy Balance:

Incoming energy = outgoing energy

Ein = Eout

Eout

Ein

Energy Balance:Ein = Eout

Ein = So re2 (1-A)

Eout

Ein

Energy Balance:Ein = Eout

Ein = So re2 (1-A)

Eout = T4(4 re2)

Eout

Ein

Energy Balance:Ein = Eout

So re2 (1-A) = T4 (4 re

2)

Eout

Ein

Energy Balance:Ein = Eout

So re2 (1-A) = T4 (4 re

2)

Eout

Ein

Energy Balance:Ein = Eout

So (1-A) = T4 (4)

Eout

Ein

Energy Balance:Ein = Eout

So (1-A) = T4 (4)

T4 = So(1-A) 4

Eout

Ein

T4 = So(1-A) 4

If we know So and A, we can calculate the temperature of the Earth. We call this the expected temperature (Texp). It is the temperature we would expect if Earth behaves like a blackbody.

This calculation can be done for any planet, provided we know its solar constant and albedo.

T4 = So(1-A) 4

For Earth:

So = 1370 W/m2

A = 0.31 = 5.67 x 10-8 W/m2K4

T4 = So(1-A) 4

For Earth:

So = 1370 W/m2

A = 0.31 = 5.67 x 10-8

T4 = (1370 W/m2)(1-0.31) 4 (5.67 x 10-8 W/m2K4)

T4 = So(1-A) 4

For Earth:

So = 1370 W/m2

A = 0.31 = 5.67 x 10-8

T4 = (1370 W/m2)(1-0.31) 4 (5.67 x 10-8 W/m2K4)

T4 = 4.23 x 109 (K4)

T = 254 K

Expected Temperature:

Texp = 254 K

(oC) = (K) - 273

Expected Temperature:

Texp = 254 K

(oC) = (K) - 273

So….

Texp = (254 - 273) = -19 oC

Is the Earth’s surface really -19 oC?

Is the Earth’s surface really -19 oC?

NO. The actual temperature is warmer!

The observed temperature (Tobs) is 15 oC

Calculate the average temperatures of Mars and Venus applying the Simple Global Temperature Model:

Planet Venus Earth MarsDistance from Sun(106 km

108 150 218Solar Constant (W/m2 )

2620 1370 589

Albedo (%) 76 31 25Atmospheric Pressure (atm)

90 1 0.006

Effective Temperature(K)Surface Temperature(K)

Planet Venus Earth MarsDistance from Sun(106 km

108 150 218Solar Constant (W/m2 )

2620 1370 589

Albedo (%) 76 31 25Atmospheric Pressure (atm)

90 1 0.006

Effective Temperature(K)

229 254 210

Surface Temperature(K)

750 288 218

Is the Earth’s surface really -19 oC?

NO. The actual temperature is warmer!

The observed temperature (Tobs) is 15 oC

The difference between observed and expected temperatures (T):

T = Tobs - Texp

T = 15 - (-19)

T = + 34 oC

T = + 34 oC

In other words, the Earth is 34 oC warmer than expected based on black body calculations and the known input of solar energy.

T = + 34 oC

In other words, the Earth is 34 oC warmer than expected based on black body calculations and the known input of solar energy.

This extra warmth is what we call the GREENHOUSE EFFECT.