Heat

Physics 313Professor Lee

CarknerLecture 9

Exercise #8 Piston Initial pressure: Cold position and pressure:

Hot position and pressure:

Work to lift weights: W = mgh h = 0.0447 m -0.0315 m = W = (0.3 kg)(9.8 m/s2)(0.0132 m) =

Exercise #8 Piston Work due to pressure:

Pressure is constant (102.5 kPa -99.1 kPa) = W = ∫ PdV = P V (isobaric process) diameter of piston = 32.5 mm, r = 0.01625 m A = r2 = ( 0.01625)2 = V = hA = (0.0132)(0.0008296) = 1.095X10-5 m3

W = PV = (3400)(1.095X10-5) = Compare

difference = 0.0388 – 0.03723 = average = 0.0380 J percent difference = [(0.0016)/0.0380)](100) =

Heat Capacity

The degree to which temperature is changed by heat can be expressed with:

Heat Capacity (J/K)

Specific heat (J/kg K)

Molar heat capacity (J/mol K)

Latent Heat

Heat can also cause a phase change with no temperature change

The latent heat (L) is the amount of heat needed (per mole or kg) to change phase

Vaporization and Fusion

Latent heat of fusion

Latent heat of vaporization Heat required:

Using a Heat Reservoir

Called a heat reservoir

The reservoir has a constant temperature For an isobaric process, the system

needs to be in contact with a variable temperature heat reservoir

Heat Problems

Sum all heats to get total Objects at different T will exchange heat

until at common T |Q1 |= |Q2 |= |m1c1(Tf-T1)| = |m2c2(Tf-T2)|

Heat reservoir has constant properties

Conduction

dQ / dt = -KA (dT/dx) A is cross sectional area K is thermal conductivity

High K = Low K =

K Dependencies

K depends on the molecular properties of a substance

K depends on temperature

Radiation Total energy and wavelengths of

photons depend on temperature: Larger T -- Larger T --

If = 1 substance is a blackbody

Need to find difference between emission and absorption to get net heat

Stefan-Boltzmann Law Thermal radiation:

P is the power (energy emitted per second) Stefan-Boltzmann constant:

=5.67051 X 10-8 W/m2 K4

dQ/dt = A(Tenv4 - T4)

Note that power per unit area is the flux (F in W/m2)

Blackbody Curves

Blackbody Radiation Classical physics could only describe the radiation

curve with the Rayleigh-Jeans law

Problem: ultraviolet catastrophe

In 1900 Max Planck determined the true radiation law empirically

Energy is quantized 1kT)exp(hc/

/2hcT),I(

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Convection

This will happen naturally in a fluid in a gravitational field Cold gas will contract, increase in density

and fall

What are the conditions and transport rates for convection?

Convective Energy Transport Convection physically moves mass so the heat

transfer depends on how much energy the mass contains and how fast it moves

F = vcT (J/s/m2) But this is only the material moving in one direction

F = vcT Assuming equal densities and velocities

Will it Float? Energy transport in fluids is radiative or

convective Consider a bubble of gas that is trying to rise

The density of the surrounding gas depends on the temperature gradient

i.e. if the surrounding gas cools with height faster than the bubble, the bubble will rise

Convection!

Convection? Gradient of surroundings depends on radiation The condition for convection can be written as:

Have convection when bub is small or rad is

large

Large CV means the bubble cools off slowly and stays hotter than its surroundings

Large opacity means radiation is absorbed and doesn’t

heat up upper layers very well

Structure of the Sun

Core

Radiative Zone

Convective

Zone

Photosphere

Chromosphere

Corona

Solar Granulation

Which Process? Radiation

Low density

Convection Fluid matter, low K

Conduction Solid matter